Networks

components/charts/network-graph/doc.ts

/**
 * NetworkGraph — things and the connections between them.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § CONTRACT — the oracle. Names no library, contains no code.              │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * # Shape
 *
 *     label         REQUIRED
 *     nodes         { id, label?, group?, size? }[]
 *     edges         { from, to, value? (signed −1–1), weight?, label? }[]
 *     layout?       "force" (default) | "radial" | "circular" | "tiered" |
 *                   "flow" | "grid"
 *     root?         the centre of a radial layout
 *     groups?       groups in a FIXED order: colour, shape, and tiers
 *     curved?, labels?, hulls? ({ key, label?, ids }[])
 *     onSelect?, selected?   selection
 *     aspect?, formatValue?, animation?  (default: nodes pop in)
 *
 * # Behaviour
 *
 * R1  The same input always gives the same picture, on the server and in
 *     every browser: layouts are deterministic.
 * R2  Position means what the layout says: force — nearness is a hint;
 *     radial — the ring is hops from the root; circular — nothing (so no
 *     node hides another); tiered — the group; flow — columns by longest
 *     path, every edge pointing forward; grid — nothing, in rows.
 * R3  Groups have a colour AND a shape. Size is drawn as area.
 * R4  A signed edge's hue is its sign and its opacity its strength; a
 *     weight is its width. An edge to a node that does not exist is ignored.
 * R5  Hover or focus lights a node and its neighbours and dims the rest.
 *     Selection is one tab stop: arrow keys move, Enter or Space selects,
 *     Escape clears.
 * R6  Changing the layout (or the data) moves nodes to their new places;
 *     a new node appears where it belongs.
 * R7  With hulls, the force layout gathers each group into its own region
 *     (up to five groups), so a hull outlines a place, not a scatter.
 * R8  Two tables list every node (with its connections) and every edge.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § MECHANICS — how this implementation meets the contract.                 │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * The force layout is d3-force, run synchronously for a fixed number of
 * ticks with hash-seeded starting positions and a seeded random source. A
 * force simulation is chaotic, and ECMAScript leaves cos, sin, hypot, exp,
 * and log to each engine, so none run inside it (d3's only trigonometry is
 * the starting spiral, which seeded positions replace); sqrt and arithmetic
 * are exactly specified by IEEE-754. Labels are HTML placed by percentage.
 */
export {};

components/charts/network-graph/network-graph.tsx

"use client";

import {
  useMemo,
  useRef,
  useState,
  type CSSProperties,
  type KeyboardEvent,
} from "react";

import { TBody, Td, Th, THead, Tr } from "@/components/display/table";
import type { AnimationProp } from "@/lib/motion";
import { useTweened } from "@/lib/motion/react";
import { cn } from "@/lib/utils/cn";
import { ChartLegend } from "../chart-legend";
import { radiusFor, shapePath } from "../_kernel/encode";
import { formatExact } from "../_kernel/format";
import {
  edgePath,
  graphTarget,
  hullAround,
  liveEdges,
  neighbours,
  type GraphEdge,
  type GraphLayout,
  type GraphNode,
  type Point,
} from "../_kernel/graph";
import { px } from "../_kernel/scale";
import { categoryColor, seriesShape } from "../_kernel/scatter";
import { ChartData } from "../_shared/chart-data";
import chart from "../_shared/chart.module.css";
import { useChartMotion } from "../_shared/use-chart-motion";
import styles from "./network-graph.module.css";

export type { GraphEdge, GraphLayout, GraphNode };

export type NetworkGraphProps = {
  /** Names the chart. */
  label: string;
  nodes: readonly GraphNode[];
  edges: readonly GraphEdge[];
  /** How position is decided — and so what it means. */
  layout?: GraphLayout;
  /** The centre of a radial layout. */
  root?: string;
  /** Groups in a FIXED order: colour, shape, and the tiers of a tiered
   *  layout. */
  groups?: readonly string[];
  /** Bow edges into arcs, where straight chords would overlap. */
  curved?: boolean;
  /** Print node names; off for dense graphs where they would be a wash. */
  labels?: boolean;
  /** Labelled regions drawn behind groups of nodes. */
  hulls?: readonly { key: string; label?: string; ids: readonly string[] }[];
  /** Makes nodes selectable: one tab stop, arrow keys move between nodes. */
  onSelect?: (id: string | null) => void;
  selected?: string | null;
  /** Width over height. */
  aspect?: number;
  formatValue?: (value: number) => string;
  /** Default: nodes pop in; changing the layout glides them to their new
   *  places. */
  animation?: AnimationProp;
  className?: string;
};

/** Things and the connections between them. What position means depends
 *  on the layout — a force layout's nearness is a hint, a radial ring is a
 *  hop count — so choose the layout for the question. Hover or focus a node
 *  to light its neighbours; the tables list every node and connection. */
export function NetworkGraph({
  label,
  nodes,
  edges: rawEdges,
  layout = "force",
  root,
  groups: groupOrder,
  curved = false,
  labels = true,
  hulls = [],
  onSelect,
  selected = null,
  aspect = 1.6,
  formatValue = formatExact,
  animation,
  className,
}: NetworkGraphProps) {
  const { rootProps, update } = useChartMotion(animation, {
    enter: "pop",
    axis: "y",
  });
  const edges = useMemo(() => liveEdges(nodes, rawEdges), [nodes, rawEdges]);
  const groups = useMemo(
    () =>
      groupOrder ??
      [...new Set(nodes.map((n) => n.group ?? ""))].filter(Boolean),
    [groupOrder, nodes],
  );
  // The layout is computed once per input, not per hover or tween frame.
  const target = useMemo(
    () =>
      graphTarget(nodes, edges, layout, aspect, {
        root,
        groups,
        // With hulls the groups are the point, so the force layout gathers
        // each into its own region.
        cluster: hulls.length > 0,
      }),
    [nodes, edges, layout, aspect, root, groups, hulls.length],
  );
  const shown = useTweened(target, update, "target");
  const near = useMemo(() => neighbours(nodes, edges), [nodes, edges]);

  const [pointed, setPointed] = useState<string | null>(null);
  const [active, setActive] = useState(0);
  const svg = useRef<SVGSVGElement>(null);
  const lit = pointed ?? selected;
  const stateOf = (id: string) =>
    lit === null
      ? undefined
      : id === lit
        ? "lit"
        : near.get(lit)?.has(id)
          ? "near"
          : "dim";

  // The frame fits the laid-out nodes, with room for their labels.
  const at = (id: string): Point | null => {
    const x = shown[`${id}|x`];
    const y = shown[`${id}|y`];
    return x === undefined || y === undefined ? null : { x, y };
  };
  const finals = nodes.flatMap((n) => {
    const x = target[`${n.id}|x`];
    const y = target[`${n.id}|y`];
    return x === undefined ? [] : [{ x, y }];
  });
  const left = Math.min(0, ...finals.map((p) => p.x)) - 60;
  const right = Math.max(1000, ...finals.map((p) => p.x)) + 60;
  const top = Math.min(0, ...finals.map((p) => p.y)) - 50;
  const bottom = Math.max(1000 / aspect, ...finals.map((p) => p.y)) + 50;
  const width = right - left;
  const height = bottom - top;
  const pct = (p: Point) => ({
    left: `${((p.x - left) / width) * 100}%`,
    top: `${((p.y - top) / height) * 100}%`,
  });

  const sizes = nodes
    .map((n) => n.size)
    .filter((s): s is number => typeof s === "number" && s > 0);
  const range: [number, number] = sizes.length
    ? [Math.min(...sizes), Math.max(...sizes)]
    : [1, 1];
  const radius = (n: GraphNode) =>
    n.size && n.size > 0 ? radiusFor(n.size, range, [9, 26]) : 11;
  const maxWeight = Math.max(1, ...edges.map((e) => e.weight ?? 0));
  const degree = (id: string) => near.get(id)?.size ?? 0;

  const select = (id: string) => onSelect?.(selected === id ? null : id);
  const move = (event: KeyboardEvent) => {
    if (!onSelect) return;
    const step = { ArrowRight: 1, ArrowDown: 1, ArrowLeft: -1, ArrowUp: -1 }[
      event.key
    ];
    if (event.key === "Escape") {
      onSelect(null);
      return;
    }
    if (step === undefined) return;
    event.preventDefault();
    const next = (active + step + nodes.length) % nodes.length;
    setActive(next);
    svg.current?.querySelector<SVGGElement>(`[data-index="${next}"]`)?.focus();
  };

  if (!nodes.length)
    return (
      <div className={cn(chart.root, className)}>
        <p className={chart.empty}>No data to display.</p>
      </div>
    );

  return (
    <div {...rootProps} className={cn(chart.root, className)}>
      {groups.length > 1 ? (
        <ChartLegend
          items={groups.map((group) => ({
            key: group,
            label: group,
            color: categoryColor(groups, group),
            shape: seriesShape(groups, group),
          }))}
        />
      ) : null}
      <div
        className={styles.frame}
        style={{ "--aspect": width / height } as CSSProperties}
      >
        <svg
          ref={svg}
          className={styles.svg}
          viewBox={`${px(left)} ${px(top)} ${px(width)} ${px(height)}`}
          role={onSelect ? "group" : "img"}
          aria-label={`${label}. Every node and connection is in the data tables.`}
          data-lit={lit ? "" : undefined}
          onKeyDown={onSelect ? move : undefined}
        >
          {hulls.map((hull, index) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape ? (
              <ellipse
                key={hull.key}
                className={styles.hull}
                style={
                  {
                    "--series": categoryColor(
                      hulls.map((h) => h.key),
                      hulls[index].key,
                    ),
                  } as CSSProperties
                }
                cx={shape.cx}
                cy={shape.cy}
                rx={shape.rx}
                ry={shape.ry}
              />
            ) : null;
          })}
          {edges.map((edge, index) => {
            const a = at(edge.from);
            const b = at(edge.to);
            if (!a || !b) return null;
            const signed = typeof edge.value === "number";
            return (
              <path
                key={`${edge.from}-${edge.to}-${index}`}
                className={styles.edge}
                d={edgePath(a, b, curved)}
                data-lit={
                  lit !== null && (edge.from === lit || edge.to === lit)
                    ? ""
                    : undefined
                }
                data-sign={
                  signed
                    ? (edge.value as number) < 0
                      ? "negative"
                      : "positive"
                    : undefined
                }
                style={
                  {
                    "--edge-w": 1 + ((edge.weight ?? 0) / maxWeight) * 3,
                    "--edge-o": signed
                      ? 0.25 +
                        Math.min(1, Math.abs(edge.value as number)) * 0.65
                      : undefined,
                  } as CSSProperties
                }
              />
            );
          })}
          {nodes.map((node, index) => {
            const p = at(node.id);
            if (!p) return null;
            const r = radius(node);
            const name = node.label ?? node.id;
            return (
              <g key={node.id} transform={`translate(${px(p.x)} ${px(p.y)})`}>
                <g
                  data-mark
                  data-index={index}
                  data-state={stateOf(node.id)}
                  className={styles.node}
                  style={
                    {
                      "--series": categoryColor(groups, node.group),
                    } as CSSProperties
                  }
                  onPointerEnter={() => setPointed(node.id)}
                  onPointerLeave={() => setPointed(null)}
                  onFocus={() => {
                    setPointed(node.id);
                    setActive(index);
                  }}
                  onBlur={() => setPointed(null)}
                  {...(onSelect
                    ? {
                        role: "button",
                        tabIndex: index === active ? 0 : -1,
                        "aria-label": `${name}${node.group ? `, ${node.group}` : ""}, ${degree(node.id)} connections`,
                        "aria-pressed": selected === node.id,
                        onClick: () => select(node.id),
                        onKeyDown: (event: KeyboardEvent) => {
                          if (event.key === "Enter" || event.key === " ") {
                            event.preventDefault();
                            select(node.id);
                          }
                        },
                      }
                    : {})}
                >
                  <circle className={styles.ring} r={r + 5} />
                  <path
                    className={styles.shape}
                    d={shapePath(seriesShape(groups, node.group), r)}
                  />
                </g>
              </g>
            );
          })}
        </svg>
        <div className={styles.labels} aria-hidden="true">
          {hulls.map((hull) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape && hull.label ? (
              <span
                key={hull.key}
                data-hull
                style={pct({ x: shape.cx, y: shape.cy - shape.ry })}
              >
                {hull.label}
              </span>
            ) : null;
          })}
          {labels
            ? nodes.map((node) => {
                const p = at(node.id);
                return p ? (
                  <span
                    key={node.id}
                    data-state={stateOf(node.id)}
                    style={pct({ x: p.x, y: p.y + radius(node) })}
                  >
                    {node.label ?? node.id}
                  </span>
                ) : null;
              })
            : null}
        </div>
      </div>
      <ChartData label={label} summary="View nodes">
        <THead>
          <Tr>
            <Th>Node</Th>
            <Th>Group</Th>
            <Th numeric>Connections</Th>
            {sizes.length ? <Th numeric>Size</Th> : null}
          </Tr>
        </THead>
        <TBody>
          {nodes.map((node) => (
            <Tr key={node.id}>
              <Th scope="row">{node.label ?? node.id}</Th>
              <Td>{node.group ?? "—"}</Td>
              <Td numeric>{degree(node.id)}</Td>
              {sizes.length ? (
                <Td numeric>
                  {typeof node.size === "number" ? formatValue(node.size) : "—"}
                </Td>
              ) : null}
            </Tr>
          ))}
        </TBody>
      </ChartData>
      <ChartData label={label} summary="View connections">
        <THead>
          <Tr>
            <Th>From</Th>
            <Th>To</Th>
            <Th numeric>Value</Th>
          </Tr>
        </THead>
        <TBody>
          {edges.map((edge, index) => {
            const name = (id: string) =>
              nodes.find((n) => n.id === id)?.label ?? id;
            const value = edge.value ?? edge.weight;
            return (
              <Tr key={index}>
                <Th scope="row">{name(edge.from)}</Th>
                <Td>{name(edge.to)}</Td>
                <Td numeric>
                  {typeof value === "number" ? formatValue(value) : "—"}
                </Td>
              </Tr>
            );
          })}
        </TBody>
      </ChartData>
    </div>
  );
}

components/charts/network-graph/network-graph.module.css

@layer primitive {
  .frame {
    position: relative;
    width: 100%;
    aspect-ratio: var(--aspect, 1.6);
  }
  .svg {
    position: absolute;
    inset: 0;
    width: 100%;
    height: 100%;
    overflow: visible;
  }
  .hull {
    fill: color-mix(in oklab, var(--series) 12%, transparent);
    stroke: color-mix(in oklab, var(--series) 45%, transparent);
    stroke-dasharray: 4 4;
    stroke-width: 1;
    vector-effect: non-scaling-stroke;
  }
  .edge {
    fill: none;
    stroke: var(--chart-axis, var(--line-strong));
    stroke-opacity: 0.7;
    stroke-width: var(--edge-w, 1.25);
    vector-effect: non-scaling-stroke;
    transition: stroke-opacity var(--dur-2) var(--ease);
  }
  .edge[data-sign="positive"] {
    stroke: var(--chart-pos);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .edge[data-sign="negative"] {
    stroke: var(--chart-neg);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .svg[data-lit] .edge:not([data-lit]) {
    stroke-opacity: 0.12;
  }
  .node {
    transform-origin: center;
    transition: opacity var(--dur-2) var(--ease);
  }
  .shape {
    fill: var(--series);
    stroke: var(--surface-panel);
    stroke-width: 1.5;
    vector-effect: non-scaling-stroke;
  }
  .svg[data-lit] .node[data-state="dim"] {
    opacity: 0.25;
  }
  .ring {
    fill: none;
    stroke: var(--accent);
    stroke-width: 2.5;
    vector-effect: non-scaling-stroke;
    opacity: 0;
  }
  .node[data-state="lit"] .ring,
  .node[aria-pressed="true"] .ring {
    opacity: 1;
  }
  .node[role="button"] {
    cursor: pointer;
    outline: none;
  }
  .node[role="button"]:focus-visible .ring {
    stroke-dasharray: 3 2;
    opacity: 1;
  }
  .labels {
    position: absolute;
    inset: 0;
    pointer-events: none;
    font-size: var(--text-11);
  }
  .labels span {
    position: absolute;
    color: var(--ink-2);
    white-space: nowrap;
    transform: translate(-50%, 6px);
    transition: opacity var(--dur-2) var(--ease);
  }
  .labels span[data-state="dim"] {
    opacity: 0.25;
  }
  .labels span[data-hull] {
    color: var(--ink-3);
    font-weight: var(--weight-medium);
    transform: translate(-50%, -100%);
  }
}

components/charts/_kernel/graph.ts

import {
  forceCollide,
  forceLink,
  forceManyBody,
  forceSimulation,
  forceX,
  forceY,
  type SimulationNodeDatum,
} from "d3-force";

import { px } from "./scale";

/* NetworkGraph's maths: layouts and geometry, all deterministic, so the
   server and the browser draw the same picture.

   A force layout is chaotic: a one-bit difference in step one grows into a
   visibly different graph. ECMAScript leaves cos, sin, hypot, exp, and log
   to each engine, so none of them appear inside the simulation — starting
   positions come from a hash, the simulation's randomness from a seeded
   generator, and distances from sqrt, which IEEE-754 specifies exactly. */

export type GraphNode = {
  id: string;
  label?: string;
  /** A class: sets colour and shape (by `groups` order), and the tier in a
   *  tiered layout. */
  group?: string;
  /** A magnitude drawn as the node's area. */
  size?: number;
};

export type GraphEdge = {
  from: string;
  to: string;
  /** Signed, −1 to 1: hue is the sign, opacity the strength. */
  value?: number;
  /** Unsigned strength: drawn as width. */
  weight?: number;
  label?: string;
};

export type GraphLayout =
  "force" | "radial" | "circular" | "tiered" | "flow" | "grid";
export type Point = { x: number; y: number };

/** The virtual canvas layouts place nodes on. */
export const GRAPH_W = 1000;

/** FNV-1a → 0–1: a repeatable number per string. */
export function seedOf(text: string) {
  let h = 2166136261;
  for (let i = 0; i < text.length; i++) {
    h ^= text.charCodeAt(i);
    h = Math.imul(h, 16777619);
  }
  return (h >>> 0) / 4294967296;
}

/** A seeded linear congruential generator for the simulation's jiggle. */
function lcg(seed: number) {
  let s = Math.floor(seed * 4294967296) >>> 0 || 1;
  return () => {
    s = (Math.imul(1664525, s) + 1013904223) >>> 0;
    return s / 4294967296;
  };
}

/** Edges whose ends both exist; a dangling edge is ignored, not guessed. */
export function liveEdges(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const ids = new Set(nodes.map((n) => n.id));
  return edges.filter(
    (e) => ids.has(e.from) && ids.has(e.to) && e.from !== e.to,
  );
}

export function neighbours(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const near = new Map<string, Set<string>>(
    nodes.map((n) => [n.id, new Set()]),
  );
  for (const e of edges) {
    near.get(e.from)?.add(e.to);
    near.get(e.to)?.add(e.from);
  }
  return near;
}

/** Hops from a root, walking edges both ways; unreached nodes go one ring
 *  beyond the furthest. */
export function hopsFrom(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  root: string,
) {
  const near = neighbours(nodes, edges);
  const depth = new Map<string, number>([[root, 0]]);
  let frontier = [root];
  while (frontier.length) {
    const next: string[] = [];
    for (const id of frontier)
      for (const other of near.get(id) ?? []) {
        if (depth.has(other)) continue;
        depth.set(other, (depth.get(id) ?? 0) + 1);
        next.push(other);
      }
    frontier = next;
  }
  const beyond = Math.max(0, ...depth.values()) + 1;
  for (const n of nodes) if (!depth.has(n.id)) depth.set(n.id, beyond);
  return depth;
}

/** Split edges into those that keep the graph acyclic and the "back"
 *  edges that close a loop, by depth-first search in input order: a loop is
 *  broken at the edge that closes it (c → a in a → b → c → a), not wherever
 *  a walk happens to land. */
export function splitLoops<E extends { from: string; to: string }>(
  nodes: readonly { id: string }[],
  edges: readonly E[],
) {
  const outgoing = new Map<string, E[]>(nodes.map((n) => [n.id, []]));
  for (const e of edges) outgoing.get(e.from)?.push(e);
  const state = new Map<string, 1 | 2>();
  const back = new Set<E>();
  const visit = (id: string) => {
    state.set(id, 1);
    for (const e of outgoing.get(id) ?? []) {
      const s = state.get(e.to);
      if (s === 1) back.add(e);
      else if (s === undefined) visit(e.to);
    }
    state.set(id, 2);
  };
  for (const n of nodes) if (!state.has(n.id)) visit(n.id);
  return {
    forward: edges.filter((e) => !back.has(e)),
    loops: edges.filter((e) => back.has(e)),
  };
}

/** Longest path from any source, for flow layouts; loops are broken first
 *  (see splitLoops). */
export function longestPath(
  nodes: readonly { id: string }[],
  edges: readonly { from: string; to: string }[],
) {
  const { forward } = splitLoops(nodes, edges);
  const incoming = new Map<string, string[]>(nodes.map((n) => [n.id, []]));
  for (const e of forward) incoming.get(e.to)?.push(e.from);
  const depth = new Map<string, number>();
  const walk = (id: string): number => {
    const known = depth.get(id);
    if (known !== undefined) return known;
    const from = incoming.get(id) ?? [];
    const d = from.length ? Math.max(...from.map((f) => walk(f) + 1)) : 0;
    depth.set(id, d);
    return d;
  };
  for (const n of nodes) walk(n.id);
  return depth;
}

type Options = { root?: string; groups: readonly string[]; cluster?: boolean };

type Layout = (
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  height: number,
  options: Options,
) => Map<string, Point>;

/** Where each group gathers when a force layout is clustered, as fractions
 *  of the canvas. A fixed table, not points on a circle: anything that feeds
 *  the simulation must avoid engine-dependent maths. */
const ANCHORS: readonly (readonly [number, number])[][] = [
  [[0.5, 0.5]],
  [
    [0.28, 0.5],
    [0.72, 0.5],
  ],
  [
    [0.5, 0.26],
    [0.26, 0.72],
    [0.74, 0.72],
  ],
  [
    [0.28, 0.28],
    [0.72, 0.28],
    [0.28, 0.72],
    [0.72, 0.72],
  ],
  [
    [0.5, 0.2],
    [0.2, 0.45],
    [0.8, 0.45],
    [0.32, 0.8],
    [0.68, 0.8],
  ],
];

const force: Layout = (nodes, edges, height, { groups, cluster }) => {
  type Sim = SimulationNodeDatum & { id: string };
  const sim: Sim[] = nodes.map((n) => ({
    id: n.id,
    x: GRAPH_W * (0.25 + seedOf(`${n.id}:x`) * 0.5),
    y: height * (0.25 + seedOf(`${n.id}:y`) * 0.5),
  }));
  const spacing = Math.sqrt((GRAPH_W * height) / Math.max(1, nodes.length));
  const simulation = forceSimulation(sim)
    .randomSource(lcg(seedOf(nodes.map((n) => n.id).join("|"))))
    .force(
      "link",
      forceLink<Sim, { source: string; target: string }>(
        edges.map((e) => ({ source: e.from, target: e.to })),
      )
        .id((d) => d.id)
        .distance(spacing * 0.55),
    )
    .force("charge", forceManyBody().strength(-spacing * 2))
    .force("collide", forceCollide(24))
    .stop();
  // Clustered, each group is drawn toward its own region (up to five
  // groups); otherwise everything is drawn gently toward the centre.
  const table = ANCHORS[Math.min(groups.length, ANCHORS.length) - 1];
  const groupOf = new Map(nodes.map((n) => [n.id, n.group ?? ""]));
  const anchor = (id: string) => {
    const index = groups.indexOf(groupOf.get(id) ?? "");
    return cluster && table && index >= 0 && index < table.length
      ? table[index]
      : [0.5, 0.5];
  };
  const pull = cluster ? 0.18 : 0.06;
  simulation
    .force("x", forceX<Sim>((d) => anchor(d.id)[0] * GRAPH_W).strength(pull))
    .force(
      "y",
      forceY<Sim>((d) => anchor(d.id)[1] * height).strength(
        pull * (GRAPH_W / height),
      ),
    );
  simulation.tick(300);
  return fit(
    new Map(sim.map((n) => [n.id, { x: n.x ?? 0, y: n.y ?? 0 }])),
    height,
  );
};

/** Scale positions uniformly (so shapes keep their proportions) to fill the
 *  canvas, less a margin for labels. */
function fit(points: Map<string, Point>, height: number, margin = 70) {
  if (points.size < 2)
    return new Map(
      [...points].map(([id]) => [id, { x: GRAPH_W / 2, y: height / 2 }]),
    );
  const xs = [...points.values()].map((p) => p.x);
  const ys = [...points.values()].map((p) => p.y);
  const [x0, x1, y0, y1] = [
    Math.min(...xs),
    Math.max(...xs),
    Math.min(...ys),
    Math.max(...ys),
  ];
  const scale = Math.min(
    (GRAPH_W - 2 * margin) / Math.max(1, x1 - x0),
    (height - 2 * margin) / Math.max(1, y1 - y0),
  );
  const ox = (GRAPH_W - (x1 - x0) * scale) / 2;
  const oy = (height - (y1 - y0) * scale) / 2;
  return new Map(
    [...points].map(([id, p]) => [
      id,
      { x: px(ox + (p.x - x0) * scale), y: px(oy + (p.y - y0) * scale) },
    ]),
  );
}

const circle = (
  count: number,
  index: number,
  cx: number,
  cy: number,
  r: number,
  turn = 0,
) => {
  const angle = (index / Math.max(1, count)) * 2 * Math.PI - Math.PI / 2 + turn;
  return { x: px(cx + r * Math.cos(angle)), y: px(cy + r * Math.sin(angle)) };
};

const radial: Layout = (nodes, edges, height, { root }) => {
  const centre = root ?? nodes[0]?.id ?? "";
  const depth = hopsFrom(nodes, edges, centre);
  const near = neighbours(nodes, edges);
  const rings = new Map<number, string[]>();
  for (const n of nodes) {
    if (n.id === centre) continue;
    const d = depth.get(n.id) ?? 1;
    rings.set(d, [...(rings.get(d) ?? []), n.id]);
  }
  const out = new Map<string, Point>([
    [centre, { x: GRAPH_W / 2, y: height / 2 }],
  ]);
  // Turns around the centre, per node, so a ring can follow the one inside.
  const turn = new Map<string, number>([[centre, 0]]);
  const count = Math.max(1, rings.size);
  const outer = Math.min(GRAPH_W, height) / 2 - 50;
  for (const [ring, ids] of [...rings].sort((a, b) => a[0] - b[0])) {
    // Order a ring by where its parent sits, so children stay beside their
    // parent and edges do not cross the middle.
    const parentTurn = (id: string) => {
      const parents = [...(near.get(id) ?? [])].filter(
        (p) => turn.has(p) && (depth.get(p) ?? 0) < ring,
      );
      return parents.length ? Math.min(...parents.map((p) => turn.get(p)!)) : 1;
    };
    const ordered = [...ids].sort(
      (a, b) => parentTurn(a) - parentTurn(b) || a.localeCompare(b),
    );
    const r = (outer * ring) / count;
    ordered.forEach((id, i) => {
      const t = (i + 0.5) / ordered.length;
      turn.set(id, t);
      out.set(id, circle(1, 0, GRAPH_W / 2, height / 2, r, t * 2 * Math.PI));
    });
  }
  return out;
};

const circular: Layout = (nodes, _edges, height) => {
  const r = Math.min(GRAPH_W, height) / 2 - 40;
  return new Map(
    nodes.map((n, i) => [
      n.id,
      circle(nodes.length, i, GRAPH_W / 2, height / 2, r),
    ]),
  );
};

const tiered: Layout = (nodes, _edges, height, { groups }) => {
  const order = [
    ...new Set([...groups, ...nodes.map((n) => n.group ?? "")]),
  ].filter((g) => nodes.some((n) => (n.group ?? "") === g));
  const out = new Map<string, Point>();
  order.forEach((group, column) => {
    const ids = nodes.filter((n) => (n.group ?? "") === group).map((n) => n.id);
    const x =
      order.length === 1
        ? GRAPH_W / 2
        : 60 + (column * (GRAPH_W - 120)) / (order.length - 1);
    ids.forEach((id, i) =>
      out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
    );
  });
  return out;
};

const flow: Layout = (nodes, edges, height) => {
  const depth = longestPath(nodes, edges);
  const columns = new Map<number, string[]>();
  for (const n of nodes) {
    const d = depth.get(n.id) ?? 0;
    columns.set(d, [...(columns.get(d) ?? []), n.id]);
  }
  const count = Math.max(1, columns.size);
  const out = new Map<string, Point>();
  [...columns]
    .sort((a, b) => a[0] - b[0])
    .forEach(([, ids], column) => {
      const x =
        count === 1
          ? GRAPH_W / 2
          : 60 + (column * (GRAPH_W - 120)) / (count - 1);
      ids.forEach((id, i) =>
        out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
      );
    });
  return out;
};

const grid: Layout = (nodes, _edges, height) => {
  const cols = Math.max(
    1,
    Math.ceil(Math.sqrt(nodes.length * (GRAPH_W / height))),
  );
  const rows = Math.max(1, Math.ceil(nodes.length / cols));
  return new Map(
    nodes.map((n, i) => [
      n.id,
      {
        x: px((((i % cols) + 1) * GRAPH_W) / (cols + 1)),
        y: px(((Math.floor(i / cols) + 1) * height) / (rows + 1)),
      },
    ]),
  );
};

const LAYOUTS: Record<GraphLayout, Layout> = {
  force,
  radial,
  circular,
  tiered,
  flow,
  grid,
};

/** Every node's position, as a record for tweening: `${id}|x`, `${id}|y`. */
export function graphTarget(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  layout: GraphLayout,
  aspect: number,
  options: Options,
) {
  const height = GRAPH_W / aspect;
  const placed = nodes.length
    ? LAYOUTS[layout](nodes, edges, height, options)
    : new Map();
  const target: Record<string, number> = {};
  for (const [id, p] of placed) {
    target[`${id}|x`] = p.x;
    target[`${id}|y`] = p.y;
  }
  return target;
}

/** A straight edge, or a shallow arc that bows with length — straight for
 *  radial layouts, arcs where chords would overlap into a disc. */
export function edgePath(a: Point, b: Point, curved: boolean) {
  if (!curved) return `M${px(a.x)},${px(a.y)}L${px(b.x)},${px(b.y)}`;
  const dx = b.x - a.x;
  const dy = b.y - a.y;
  const distance = Math.sqrt(dx * dx + dy * dy) || 1;
  const bow = Math.min(distance * 0.18, 60);
  const mx = (a.x + b.x) / 2 - (dy / distance) * bow;
  const my = (a.y + b.y) / 2 + (dx / distance) * bow;
  return `M${px(a.x)},${px(a.y)}Q${px(mx)},${px(my)} ${px(b.x)},${px(b.y)}`;
}

/** An ellipse around a set of positions, for a labelled group (a hull). */
export function hullAround(points: readonly Point[]) {
  if (!points.length) return null;
  const cx = points.reduce((sum, p) => sum + p.x, 0) / points.length;
  const cy = points.reduce((sum, p) => sum + p.y, 0) / points.length;
  const r =
    Math.max(
      34,
      ...points.map((p) => {
        const dx = p.x - cx;
        const dy = p.y - cy;
        return Math.sqrt(dx * dx + dy * dy);
      }),
    ) + 30;
  return { cx: px(cx), cy: px(cy), rx: px(r * 1.12), ry: px(r) };
}

components/charts/network-graph/doc.ts

/**
 * NetworkGraph — things and the connections between them.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § CONTRACT — the oracle. Names no library, contains no code.              │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * # Shape
 *
 *     label         REQUIRED
 *     nodes         { id, label?, group?, size? }[]
 *     edges         { from, to, value? (signed −1–1), weight?, label? }[]
 *     layout?       "force" (default) | "radial" | "circular" | "tiered" |
 *                   "flow" | "grid"
 *     root?         the centre of a radial layout
 *     groups?       groups in a FIXED order: colour, shape, and tiers
 *     curved?, labels?, hulls? ({ key, label?, ids }[])
 *     onSelect?, selected?   selection
 *     aspect?, formatValue?, animation?  (default: nodes pop in)
 *
 * # Behaviour
 *
 * R1  The same input always gives the same picture, on the server and in
 *     every browser: layouts are deterministic.
 * R2  Position means what the layout says: force — nearness is a hint;
 *     radial — the ring is hops from the root; circular — nothing (so no
 *     node hides another); tiered — the group; flow — columns by longest
 *     path, every edge pointing forward; grid — nothing, in rows.
 * R3  Groups have a colour AND a shape. Size is drawn as area.
 * R4  A signed edge's hue is its sign and its opacity its strength; a
 *     weight is its width. An edge to a node that does not exist is ignored.
 * R5  Hover or focus lights a node and its neighbours and dims the rest.
 *     Selection is one tab stop: arrow keys move, Enter or Space selects,
 *     Escape clears.
 * R6  Changing the layout (or the data) moves nodes to their new places;
 *     a new node appears where it belongs.
 * R7  With hulls, the force layout gathers each group into its own region
 *     (up to five groups), so a hull outlines a place, not a scatter.
 * R8  Two tables list every node (with its connections) and every edge.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § MECHANICS — how this implementation meets the contract.                 │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * The force layout is d3-force, run synchronously for a fixed number of
 * ticks with hash-seeded starting positions and a seeded random source. A
 * force simulation is chaotic, and ECMAScript leaves cos, sin, hypot, exp,
 * and log to each engine, so none run inside it (d3's only trigonometry is
 * the starting spiral, which seeded positions replace); sqrt and arithmetic
 * are exactly specified by IEEE-754. Labels are HTML placed by percentage.
 */
export {};

components/charts/network-graph/network-graph.tsx

"use client";

import {
  useMemo,
  useRef,
  useState,
  type CSSProperties,
  type KeyboardEvent,
} from "react";

import { TBody, Td, Th, THead, Tr } from "@/components/display/table";
import type { AnimationProp } from "@/lib/motion";
import { useTweened } from "@/lib/motion/react";
import { cn } from "@/lib/utils/cn";
import { ChartLegend } from "../chart-legend";
import { radiusFor, shapePath } from "../_kernel/encode";
import { formatExact } from "../_kernel/format";
import {
  edgePath,
  graphTarget,
  hullAround,
  liveEdges,
  neighbours,
  type GraphEdge,
  type GraphLayout,
  type GraphNode,
  type Point,
} from "../_kernel/graph";
import { px } from "../_kernel/scale";
import { categoryColor, seriesShape } from "../_kernel/scatter";
import { ChartData } from "../_shared/chart-data";
import chart from "../_shared/chart.module.css";
import { useChartMotion } from "../_shared/use-chart-motion";
import styles from "./network-graph.module.css";

export type { GraphEdge, GraphLayout, GraphNode };

export type NetworkGraphProps = {
  /** Names the chart. */
  label: string;
  nodes: readonly GraphNode[];
  edges: readonly GraphEdge[];
  /** How position is decided — and so what it means. */
  layout?: GraphLayout;
  /** The centre of a radial layout. */
  root?: string;
  /** Groups in a FIXED order: colour, shape, and the tiers of a tiered
   *  layout. */
  groups?: readonly string[];
  /** Bow edges into arcs, where straight chords would overlap. */
  curved?: boolean;
  /** Print node names; off for dense graphs where they would be a wash. */
  labels?: boolean;
  /** Labelled regions drawn behind groups of nodes. */
  hulls?: readonly { key: string; label?: string; ids: readonly string[] }[];
  /** Makes nodes selectable: one tab stop, arrow keys move between nodes. */
  onSelect?: (id: string | null) => void;
  selected?: string | null;
  /** Width over height. */
  aspect?: number;
  formatValue?: (value: number) => string;
  /** Default: nodes pop in; changing the layout glides them to their new
   *  places. */
  animation?: AnimationProp;
  className?: string;
};

/** Things and the connections between them. What position means depends
 *  on the layout — a force layout's nearness is a hint, a radial ring is a
 *  hop count — so choose the layout for the question. Hover or focus a node
 *  to light its neighbours; the tables list every node and connection. */
export function NetworkGraph({
  label,
  nodes,
  edges: rawEdges,
  layout = "force",
  root,
  groups: groupOrder,
  curved = false,
  labels = true,
  hulls = [],
  onSelect,
  selected = null,
  aspect = 1.6,
  formatValue = formatExact,
  animation,
  className,
}: NetworkGraphProps) {
  const { rootProps, update } = useChartMotion(animation, {
    enter: "pop",
    axis: "y",
  });
  const edges = useMemo(() => liveEdges(nodes, rawEdges), [nodes, rawEdges]);
  const groups = useMemo(
    () =>
      groupOrder ??
      [...new Set(nodes.map((n) => n.group ?? ""))].filter(Boolean),
    [groupOrder, nodes],
  );
  // The layout is computed once per input, not per hover or tween frame.
  const target = useMemo(
    () =>
      graphTarget(nodes, edges, layout, aspect, {
        root,
        groups,
        // With hulls the groups are the point, so the force layout gathers
        // each into its own region.
        cluster: hulls.length > 0,
      }),
    [nodes, edges, layout, aspect, root, groups, hulls.length],
  );
  const shown = useTweened(target, update, "target");
  const near = useMemo(() => neighbours(nodes, edges), [nodes, edges]);

  const [pointed, setPointed] = useState<string | null>(null);
  const [active, setActive] = useState(0);
  const svg = useRef<SVGSVGElement>(null);
  const lit = pointed ?? selected;
  const stateOf = (id: string) =>
    lit === null
      ? undefined
      : id === lit
        ? "lit"
        : near.get(lit)?.has(id)
          ? "near"
          : "dim";

  // The frame fits the laid-out nodes, with room for their labels.
  const at = (id: string): Point | null => {
    const x = shown[`${id}|x`];
    const y = shown[`${id}|y`];
    return x === undefined || y === undefined ? null : { x, y };
  };
  const finals = nodes.flatMap((n) => {
    const x = target[`${n.id}|x`];
    const y = target[`${n.id}|y`];
    return x === undefined ? [] : [{ x, y }];
  });
  const left = Math.min(0, ...finals.map((p) => p.x)) - 60;
  const right = Math.max(1000, ...finals.map((p) => p.x)) + 60;
  const top = Math.min(0, ...finals.map((p) => p.y)) - 50;
  const bottom = Math.max(1000 / aspect, ...finals.map((p) => p.y)) + 50;
  const width = right - left;
  const height = bottom - top;
  const pct = (p: Point) => ({
    left: `${((p.x - left) / width) * 100}%`,
    top: `${((p.y - top) / height) * 100}%`,
  });

  const sizes = nodes
    .map((n) => n.size)
    .filter((s): s is number => typeof s === "number" && s > 0);
  const range: [number, number] = sizes.length
    ? [Math.min(...sizes), Math.max(...sizes)]
    : [1, 1];
  const radius = (n: GraphNode) =>
    n.size && n.size > 0 ? radiusFor(n.size, range, [9, 26]) : 11;
  const maxWeight = Math.max(1, ...edges.map((e) => e.weight ?? 0));
  const degree = (id: string) => near.get(id)?.size ?? 0;

  const select = (id: string) => onSelect?.(selected === id ? null : id);
  const move = (event: KeyboardEvent) => {
    if (!onSelect) return;
    const step = { ArrowRight: 1, ArrowDown: 1, ArrowLeft: -1, ArrowUp: -1 }[
      event.key
    ];
    if (event.key === "Escape") {
      onSelect(null);
      return;
    }
    if (step === undefined) return;
    event.preventDefault();
    const next = (active + step + nodes.length) % nodes.length;
    setActive(next);
    svg.current?.querySelector<SVGGElement>(`[data-index="${next}"]`)?.focus();
  };

  if (!nodes.length)
    return (
      <div className={cn(chart.root, className)}>
        <p className={chart.empty}>No data to display.</p>
      </div>
    );

  return (
    <div {...rootProps} className={cn(chart.root, className)}>
      {groups.length > 1 ? (
        <ChartLegend
          items={groups.map((group) => ({
            key: group,
            label: group,
            color: categoryColor(groups, group),
            shape: seriesShape(groups, group),
          }))}
        />
      ) : null}
      <div
        className={styles.frame}
        style={{ "--aspect": width / height } as CSSProperties}
      >
        <svg
          ref={svg}
          className={styles.svg}
          viewBox={`${px(left)} ${px(top)} ${px(width)} ${px(height)}`}
          role={onSelect ? "group" : "img"}
          aria-label={`${label}. Every node and connection is in the data tables.`}
          data-lit={lit ? "" : undefined}
          onKeyDown={onSelect ? move : undefined}
        >
          {hulls.map((hull, index) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape ? (
              <ellipse
                key={hull.key}
                className={styles.hull}
                style={
                  {
                    "--series": categoryColor(
                      hulls.map((h) => h.key),
                      hulls[index].key,
                    ),
                  } as CSSProperties
                }
                cx={shape.cx}
                cy={shape.cy}
                rx={shape.rx}
                ry={shape.ry}
              />
            ) : null;
          })}
          {edges.map((edge, index) => {
            const a = at(edge.from);
            const b = at(edge.to);
            if (!a || !b) return null;
            const signed = typeof edge.value === "number";
            return (
              <path
                key={`${edge.from}-${edge.to}-${index}`}
                className={styles.edge}
                d={edgePath(a, b, curved)}
                data-lit={
                  lit !== null && (edge.from === lit || edge.to === lit)
                    ? ""
                    : undefined
                }
                data-sign={
                  signed
                    ? (edge.value as number) < 0
                      ? "negative"
                      : "positive"
                    : undefined
                }
                style={
                  {
                    "--edge-w": 1 + ((edge.weight ?? 0) / maxWeight) * 3,
                    "--edge-o": signed
                      ? 0.25 +
                        Math.min(1, Math.abs(edge.value as number)) * 0.65
                      : undefined,
                  } as CSSProperties
                }
              />
            );
          })}
          {nodes.map((node, index) => {
            const p = at(node.id);
            if (!p) return null;
            const r = radius(node);
            const name = node.label ?? node.id;
            return (
              <g key={node.id} transform={`translate(${px(p.x)} ${px(p.y)})`}>
                <g
                  data-mark
                  data-index={index}
                  data-state={stateOf(node.id)}
                  className={styles.node}
                  style={
                    {
                      "--series": categoryColor(groups, node.group),
                    } as CSSProperties
                  }
                  onPointerEnter={() => setPointed(node.id)}
                  onPointerLeave={() => setPointed(null)}
                  onFocus={() => {
                    setPointed(node.id);
                    setActive(index);
                  }}
                  onBlur={() => setPointed(null)}
                  {...(onSelect
                    ? {
                        role: "button",
                        tabIndex: index === active ? 0 : -1,
                        "aria-label": `${name}${node.group ? `, ${node.group}` : ""}, ${degree(node.id)} connections`,
                        "aria-pressed": selected === node.id,
                        onClick: () => select(node.id),
                        onKeyDown: (event: KeyboardEvent) => {
                          if (event.key === "Enter" || event.key === " ") {
                            event.preventDefault();
                            select(node.id);
                          }
                        },
                      }
                    : {})}
                >
                  <circle className={styles.ring} r={r + 5} />
                  <path
                    className={styles.shape}
                    d={shapePath(seriesShape(groups, node.group), r)}
                  />
                </g>
              </g>
            );
          })}
        </svg>
        <div className={styles.labels} aria-hidden="true">
          {hulls.map((hull) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape && hull.label ? (
              <span
                key={hull.key}
                data-hull
                style={pct({ x: shape.cx, y: shape.cy - shape.ry })}
              >
                {hull.label}
              </span>
            ) : null;
          })}
          {labels
            ? nodes.map((node) => {
                const p = at(node.id);
                return p ? (
                  <span
                    key={node.id}
                    data-state={stateOf(node.id)}
                    style={pct({ x: p.x, y: p.y + radius(node) })}
                  >
                    {node.label ?? node.id}
                  </span>
                ) : null;
              })
            : null}
        </div>
      </div>
      <ChartData label={label} summary="View nodes">
        <THead>
          <Tr>
            <Th>Node</Th>
            <Th>Group</Th>
            <Th numeric>Connections</Th>
            {sizes.length ? <Th numeric>Size</Th> : null}
          </Tr>
        </THead>
        <TBody>
          {nodes.map((node) => (
            <Tr key={node.id}>
              <Th scope="row">{node.label ?? node.id}</Th>
              <Td>{node.group ?? "—"}</Td>
              <Td numeric>{degree(node.id)}</Td>
              {sizes.length ? (
                <Td numeric>
                  {typeof node.size === "number" ? formatValue(node.size) : "—"}
                </Td>
              ) : null}
            </Tr>
          ))}
        </TBody>
      </ChartData>
      <ChartData label={label} summary="View connections">
        <THead>
          <Tr>
            <Th>From</Th>
            <Th>To</Th>
            <Th numeric>Value</Th>
          </Tr>
        </THead>
        <TBody>
          {edges.map((edge, index) => {
            const name = (id: string) =>
              nodes.find((n) => n.id === id)?.label ?? id;
            const value = edge.value ?? edge.weight;
            return (
              <Tr key={index}>
                <Th scope="row">{name(edge.from)}</Th>
                <Td>{name(edge.to)}</Td>
                <Td numeric>
                  {typeof value === "number" ? formatValue(value) : "—"}
                </Td>
              </Tr>
            );
          })}
        </TBody>
      </ChartData>
    </div>
  );
}

components/charts/network-graph/network-graph.module.css

@layer primitive {
  .frame {
    position: relative;
    width: 100%;
    aspect-ratio: var(--aspect, 1.6);
  }
  .svg {
    position: absolute;
    inset: 0;
    width: 100%;
    height: 100%;
    overflow: visible;
  }
  .hull {
    fill: color-mix(in oklab, var(--series) 12%, transparent);
    stroke: color-mix(in oklab, var(--series) 45%, transparent);
    stroke-dasharray: 4 4;
    stroke-width: 1;
    vector-effect: non-scaling-stroke;
  }
  .edge {
    fill: none;
    stroke: var(--chart-axis, var(--line-strong));
    stroke-opacity: 0.7;
    stroke-width: var(--edge-w, 1.25);
    vector-effect: non-scaling-stroke;
    transition: stroke-opacity var(--dur-2) var(--ease);
  }
  .edge[data-sign="positive"] {
    stroke: var(--chart-pos);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .edge[data-sign="negative"] {
    stroke: var(--chart-neg);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .svg[data-lit] .edge:not([data-lit]) {
    stroke-opacity: 0.12;
  }
  .node {
    transform-origin: center;
    transition: opacity var(--dur-2) var(--ease);
  }
  .shape {
    fill: var(--series);
    stroke: var(--surface-panel);
    stroke-width: 1.5;
    vector-effect: non-scaling-stroke;
  }
  .svg[data-lit] .node[data-state="dim"] {
    opacity: 0.25;
  }
  .ring {
    fill: none;
    stroke: var(--accent);
    stroke-width: 2.5;
    vector-effect: non-scaling-stroke;
    opacity: 0;
  }
  .node[data-state="lit"] .ring,
  .node[aria-pressed="true"] .ring {
    opacity: 1;
  }
  .node[role="button"] {
    cursor: pointer;
    outline: none;
  }
  .node[role="button"]:focus-visible .ring {
    stroke-dasharray: 3 2;
    opacity: 1;
  }
  .labels {
    position: absolute;
    inset: 0;
    pointer-events: none;
    font-size: var(--text-11);
  }
  .labels span {
    position: absolute;
    color: var(--ink-2);
    white-space: nowrap;
    transform: translate(-50%, 6px);
    transition: opacity var(--dur-2) var(--ease);
  }
  .labels span[data-state="dim"] {
    opacity: 0.25;
  }
  .labels span[data-hull] {
    color: var(--ink-3);
    font-weight: var(--weight-medium);
    transform: translate(-50%, -100%);
  }
}

components/charts/_kernel/graph.ts

import {
  forceCollide,
  forceLink,
  forceManyBody,
  forceSimulation,
  forceX,
  forceY,
  type SimulationNodeDatum,
} from "d3-force";

import { px } from "./scale";

/* NetworkGraph's maths: layouts and geometry, all deterministic, so the
   server and the browser draw the same picture.

   A force layout is chaotic: a one-bit difference in step one grows into a
   visibly different graph. ECMAScript leaves cos, sin, hypot, exp, and log
   to each engine, so none of them appear inside the simulation — starting
   positions come from a hash, the simulation's randomness from a seeded
   generator, and distances from sqrt, which IEEE-754 specifies exactly. */

export type GraphNode = {
  id: string;
  label?: string;
  /** A class: sets colour and shape (by `groups` order), and the tier in a
   *  tiered layout. */
  group?: string;
  /** A magnitude drawn as the node's area. */
  size?: number;
};

export type GraphEdge = {
  from: string;
  to: string;
  /** Signed, −1 to 1: hue is the sign, opacity the strength. */
  value?: number;
  /** Unsigned strength: drawn as width. */
  weight?: number;
  label?: string;
};

export type GraphLayout =
  "force" | "radial" | "circular" | "tiered" | "flow" | "grid";
export type Point = { x: number; y: number };

/** The virtual canvas layouts place nodes on. */
export const GRAPH_W = 1000;

/** FNV-1a → 0–1: a repeatable number per string. */
export function seedOf(text: string) {
  let h = 2166136261;
  for (let i = 0; i < text.length; i++) {
    h ^= text.charCodeAt(i);
    h = Math.imul(h, 16777619);
  }
  return (h >>> 0) / 4294967296;
}

/** A seeded linear congruential generator for the simulation's jiggle. */
function lcg(seed: number) {
  let s = Math.floor(seed * 4294967296) >>> 0 || 1;
  return () => {
    s = (Math.imul(1664525, s) + 1013904223) >>> 0;
    return s / 4294967296;
  };
}

/** Edges whose ends both exist; a dangling edge is ignored, not guessed. */
export function liveEdges(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const ids = new Set(nodes.map((n) => n.id));
  return edges.filter(
    (e) => ids.has(e.from) && ids.has(e.to) && e.from !== e.to,
  );
}

export function neighbours(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const near = new Map<string, Set<string>>(
    nodes.map((n) => [n.id, new Set()]),
  );
  for (const e of edges) {
    near.get(e.from)?.add(e.to);
    near.get(e.to)?.add(e.from);
  }
  return near;
}

/** Hops from a root, walking edges both ways; unreached nodes go one ring
 *  beyond the furthest. */
export function hopsFrom(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  root: string,
) {
  const near = neighbours(nodes, edges);
  const depth = new Map<string, number>([[root, 0]]);
  let frontier = [root];
  while (frontier.length) {
    const next: string[] = [];
    for (const id of frontier)
      for (const other of near.get(id) ?? []) {
        if (depth.has(other)) continue;
        depth.set(other, (depth.get(id) ?? 0) + 1);
        next.push(other);
      }
    frontier = next;
  }
  const beyond = Math.max(0, ...depth.values()) + 1;
  for (const n of nodes) if (!depth.has(n.id)) depth.set(n.id, beyond);
  return depth;
}

/** Split edges into those that keep the graph acyclic and the "back"
 *  edges that close a loop, by depth-first search in input order: a loop is
 *  broken at the edge that closes it (c → a in a → b → c → a), not wherever
 *  a walk happens to land. */
export function splitLoops<E extends { from: string; to: string }>(
  nodes: readonly { id: string }[],
  edges: readonly E[],
) {
  const outgoing = new Map<string, E[]>(nodes.map((n) => [n.id, []]));
  for (const e of edges) outgoing.get(e.from)?.push(e);
  const state = new Map<string, 1 | 2>();
  const back = new Set<E>();
  const visit = (id: string) => {
    state.set(id, 1);
    for (const e of outgoing.get(id) ?? []) {
      const s = state.get(e.to);
      if (s === 1) back.add(e);
      else if (s === undefined) visit(e.to);
    }
    state.set(id, 2);
  };
  for (const n of nodes) if (!state.has(n.id)) visit(n.id);
  return {
    forward: edges.filter((e) => !back.has(e)),
    loops: edges.filter((e) => back.has(e)),
  };
}

/** Longest path from any source, for flow layouts; loops are broken first
 *  (see splitLoops). */
export function longestPath(
  nodes: readonly { id: string }[],
  edges: readonly { from: string; to: string }[],
) {
  const { forward } = splitLoops(nodes, edges);
  const incoming = new Map<string, string[]>(nodes.map((n) => [n.id, []]));
  for (const e of forward) incoming.get(e.to)?.push(e.from);
  const depth = new Map<string, number>();
  const walk = (id: string): number => {
    const known = depth.get(id);
    if (known !== undefined) return known;
    const from = incoming.get(id) ?? [];
    const d = from.length ? Math.max(...from.map((f) => walk(f) + 1)) : 0;
    depth.set(id, d);
    return d;
  };
  for (const n of nodes) walk(n.id);
  return depth;
}

type Options = { root?: string; groups: readonly string[]; cluster?: boolean };

type Layout = (
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  height: number,
  options: Options,
) => Map<string, Point>;

/** Where each group gathers when a force layout is clustered, as fractions
 *  of the canvas. A fixed table, not points on a circle: anything that feeds
 *  the simulation must avoid engine-dependent maths. */
const ANCHORS: readonly (readonly [number, number])[][] = [
  [[0.5, 0.5]],
  [
    [0.28, 0.5],
    [0.72, 0.5],
  ],
  [
    [0.5, 0.26],
    [0.26, 0.72],
    [0.74, 0.72],
  ],
  [
    [0.28, 0.28],
    [0.72, 0.28],
    [0.28, 0.72],
    [0.72, 0.72],
  ],
  [
    [0.5, 0.2],
    [0.2, 0.45],
    [0.8, 0.45],
    [0.32, 0.8],
    [0.68, 0.8],
  ],
];

const force: Layout = (nodes, edges, height, { groups, cluster }) => {
  type Sim = SimulationNodeDatum & { id: string };
  const sim: Sim[] = nodes.map((n) => ({
    id: n.id,
    x: GRAPH_W * (0.25 + seedOf(`${n.id}:x`) * 0.5),
    y: height * (0.25 + seedOf(`${n.id}:y`) * 0.5),
  }));
  const spacing = Math.sqrt((GRAPH_W * height) / Math.max(1, nodes.length));
  const simulation = forceSimulation(sim)
    .randomSource(lcg(seedOf(nodes.map((n) => n.id).join("|"))))
    .force(
      "link",
      forceLink<Sim, { source: string; target: string }>(
        edges.map((e) => ({ source: e.from, target: e.to })),
      )
        .id((d) => d.id)
        .distance(spacing * 0.55),
    )
    .force("charge", forceManyBody().strength(-spacing * 2))
    .force("collide", forceCollide(24))
    .stop();
  // Clustered, each group is drawn toward its own region (up to five
  // groups); otherwise everything is drawn gently toward the centre.
  const table = ANCHORS[Math.min(groups.length, ANCHORS.length) - 1];
  const groupOf = new Map(nodes.map((n) => [n.id, n.group ?? ""]));
  const anchor = (id: string) => {
    const index = groups.indexOf(groupOf.get(id) ?? "");
    return cluster && table && index >= 0 && index < table.length
      ? table[index]
      : [0.5, 0.5];
  };
  const pull = cluster ? 0.18 : 0.06;
  simulation
    .force("x", forceX<Sim>((d) => anchor(d.id)[0] * GRAPH_W).strength(pull))
    .force(
      "y",
      forceY<Sim>((d) => anchor(d.id)[1] * height).strength(
        pull * (GRAPH_W / height),
      ),
    );
  simulation.tick(300);
  return fit(
    new Map(sim.map((n) => [n.id, { x: n.x ?? 0, y: n.y ?? 0 }])),
    height,
  );
};

/** Scale positions uniformly (so shapes keep their proportions) to fill the
 *  canvas, less a margin for labels. */
function fit(points: Map<string, Point>, height: number, margin = 70) {
  if (points.size < 2)
    return new Map(
      [...points].map(([id]) => [id, { x: GRAPH_W / 2, y: height / 2 }]),
    );
  const xs = [...points.values()].map((p) => p.x);
  const ys = [...points.values()].map((p) => p.y);
  const [x0, x1, y0, y1] = [
    Math.min(...xs),
    Math.max(...xs),
    Math.min(...ys),
    Math.max(...ys),
  ];
  const scale = Math.min(
    (GRAPH_W - 2 * margin) / Math.max(1, x1 - x0),
    (height - 2 * margin) / Math.max(1, y1 - y0),
  );
  const ox = (GRAPH_W - (x1 - x0) * scale) / 2;
  const oy = (height - (y1 - y0) * scale) / 2;
  return new Map(
    [...points].map(([id, p]) => [
      id,
      { x: px(ox + (p.x - x0) * scale), y: px(oy + (p.y - y0) * scale) },
    ]),
  );
}

const circle = (
  count: number,
  index: number,
  cx: number,
  cy: number,
  r: number,
  turn = 0,
) => {
  const angle = (index / Math.max(1, count)) * 2 * Math.PI - Math.PI / 2 + turn;
  return { x: px(cx + r * Math.cos(angle)), y: px(cy + r * Math.sin(angle)) };
};

const radial: Layout = (nodes, edges, height, { root }) => {
  const centre = root ?? nodes[0]?.id ?? "";
  const depth = hopsFrom(nodes, edges, centre);
  const near = neighbours(nodes, edges);
  const rings = new Map<number, string[]>();
  for (const n of nodes) {
    if (n.id === centre) continue;
    const d = depth.get(n.id) ?? 1;
    rings.set(d, [...(rings.get(d) ?? []), n.id]);
  }
  const out = new Map<string, Point>([
    [centre, { x: GRAPH_W / 2, y: height / 2 }],
  ]);
  // Turns around the centre, per node, so a ring can follow the one inside.
  const turn = new Map<string, number>([[centre, 0]]);
  const count = Math.max(1, rings.size);
  const outer = Math.min(GRAPH_W, height) / 2 - 50;
  for (const [ring, ids] of [...rings].sort((a, b) => a[0] - b[0])) {
    // Order a ring by where its parent sits, so children stay beside their
    // parent and edges do not cross the middle.
    const parentTurn = (id: string) => {
      const parents = [...(near.get(id) ?? [])].filter(
        (p) => turn.has(p) && (depth.get(p) ?? 0) < ring,
      );
      return parents.length ? Math.min(...parents.map((p) => turn.get(p)!)) : 1;
    };
    const ordered = [...ids].sort(
      (a, b) => parentTurn(a) - parentTurn(b) || a.localeCompare(b),
    );
    const r = (outer * ring) / count;
    ordered.forEach((id, i) => {
      const t = (i + 0.5) / ordered.length;
      turn.set(id, t);
      out.set(id, circle(1, 0, GRAPH_W / 2, height / 2, r, t * 2 * Math.PI));
    });
  }
  return out;
};

const circular: Layout = (nodes, _edges, height) => {
  const r = Math.min(GRAPH_W, height) / 2 - 40;
  return new Map(
    nodes.map((n, i) => [
      n.id,
      circle(nodes.length, i, GRAPH_W / 2, height / 2, r),
    ]),
  );
};

const tiered: Layout = (nodes, _edges, height, { groups }) => {
  const order = [
    ...new Set([...groups, ...nodes.map((n) => n.group ?? "")]),
  ].filter((g) => nodes.some((n) => (n.group ?? "") === g));
  const out = new Map<string, Point>();
  order.forEach((group, column) => {
    const ids = nodes.filter((n) => (n.group ?? "") === group).map((n) => n.id);
    const x =
      order.length === 1
        ? GRAPH_W / 2
        : 60 + (column * (GRAPH_W - 120)) / (order.length - 1);
    ids.forEach((id, i) =>
      out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
    );
  });
  return out;
};

const flow: Layout = (nodes, edges, height) => {
  const depth = longestPath(nodes, edges);
  const columns = new Map<number, string[]>();
  for (const n of nodes) {
    const d = depth.get(n.id) ?? 0;
    columns.set(d, [...(columns.get(d) ?? []), n.id]);
  }
  const count = Math.max(1, columns.size);
  const out = new Map<string, Point>();
  [...columns]
    .sort((a, b) => a[0] - b[0])
    .forEach(([, ids], column) => {
      const x =
        count === 1
          ? GRAPH_W / 2
          : 60 + (column * (GRAPH_W - 120)) / (count - 1);
      ids.forEach((id, i) =>
        out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
      );
    });
  return out;
};

const grid: Layout = (nodes, _edges, height) => {
  const cols = Math.max(
    1,
    Math.ceil(Math.sqrt(nodes.length * (GRAPH_W / height))),
  );
  const rows = Math.max(1, Math.ceil(nodes.length / cols));
  return new Map(
    nodes.map((n, i) => [
      n.id,
      {
        x: px((((i % cols) + 1) * GRAPH_W) / (cols + 1)),
        y: px(((Math.floor(i / cols) + 1) * height) / (rows + 1)),
      },
    ]),
  );
};

const LAYOUTS: Record<GraphLayout, Layout> = {
  force,
  radial,
  circular,
  tiered,
  flow,
  grid,
};

/** Every node's position, as a record for tweening: `${id}|x`, `${id}|y`. */
export function graphTarget(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  layout: GraphLayout,
  aspect: number,
  options: Options,
) {
  const height = GRAPH_W / aspect;
  const placed = nodes.length
    ? LAYOUTS[layout](nodes, edges, height, options)
    : new Map();
  const target: Record<string, number> = {};
  for (const [id, p] of placed) {
    target[`${id}|x`] = p.x;
    target[`${id}|y`] = p.y;
  }
  return target;
}

/** A straight edge, or a shallow arc that bows with length — straight for
 *  radial layouts, arcs where chords would overlap into a disc. */
export function edgePath(a: Point, b: Point, curved: boolean) {
  if (!curved) return `M${px(a.x)},${px(a.y)}L${px(b.x)},${px(b.y)}`;
  const dx = b.x - a.x;
  const dy = b.y - a.y;
  const distance = Math.sqrt(dx * dx + dy * dy) || 1;
  const bow = Math.min(distance * 0.18, 60);
  const mx = (a.x + b.x) / 2 - (dy / distance) * bow;
  const my = (a.y + b.y) / 2 + (dx / distance) * bow;
  return `M${px(a.x)},${px(a.y)}Q${px(mx)},${px(my)} ${px(b.x)},${px(b.y)}`;
}

/** An ellipse around a set of positions, for a labelled group (a hull). */
export function hullAround(points: readonly Point[]) {
  if (!points.length) return null;
  const cx = points.reduce((sum, p) => sum + p.x, 0) / points.length;
  const cy = points.reduce((sum, p) => sum + p.y, 0) / points.length;
  const r =
    Math.max(
      34,
      ...points.map((p) => {
        const dx = p.x - cx;
        const dy = p.y - cy;
        return Math.sqrt(dx * dx + dy * dy);
      }),
    ) + 30;
  return { cx: px(cx), cy: px(cy), rx: px(r * 1.12), ry: px(r) };
}

components/charts/network-graph/doc.ts

/**
 * NetworkGraph — things and the connections between them.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § CONTRACT — the oracle. Names no library, contains no code.              │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * # Shape
 *
 *     label         REQUIRED
 *     nodes         { id, label?, group?, size? }[]
 *     edges         { from, to, value? (signed −1–1), weight?, label? }[]
 *     layout?       "force" (default) | "radial" | "circular" | "tiered" |
 *                   "flow" | "grid"
 *     root?         the centre of a radial layout
 *     groups?       groups in a FIXED order: colour, shape, and tiers
 *     curved?, labels?, hulls? ({ key, label?, ids }[])
 *     onSelect?, selected?   selection
 *     aspect?, formatValue?, animation?  (default: nodes pop in)
 *
 * # Behaviour
 *
 * R1  The same input always gives the same picture, on the server and in
 *     every browser: layouts are deterministic.
 * R2  Position means what the layout says: force — nearness is a hint;
 *     radial — the ring is hops from the root; circular — nothing (so no
 *     node hides another); tiered — the group; flow — columns by longest
 *     path, every edge pointing forward; grid — nothing, in rows.
 * R3  Groups have a colour AND a shape. Size is drawn as area.
 * R4  A signed edge's hue is its sign and its opacity its strength; a
 *     weight is its width. An edge to a node that does not exist is ignored.
 * R5  Hover or focus lights a node and its neighbours and dims the rest.
 *     Selection is one tab stop: arrow keys move, Enter or Space selects,
 *     Escape clears.
 * R6  Changing the layout (or the data) moves nodes to their new places;
 *     a new node appears where it belongs.
 * R7  With hulls, the force layout gathers each group into its own region
 *     (up to five groups), so a hull outlines a place, not a scatter.
 * R8  Two tables list every node (with its connections) and every edge.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § MECHANICS — how this implementation meets the contract.                 │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * The force layout is d3-force, run synchronously for a fixed number of
 * ticks with hash-seeded starting positions and a seeded random source. A
 * force simulation is chaotic, and ECMAScript leaves cos, sin, hypot, exp,
 * and log to each engine, so none run inside it (d3's only trigonometry is
 * the starting spiral, which seeded positions replace); sqrt and arithmetic
 * are exactly specified by IEEE-754. Labels are HTML placed by percentage.
 */
export {};

components/charts/network-graph/network-graph.tsx

"use client";

import {
  useMemo,
  useRef,
  useState,
  type CSSProperties,
  type KeyboardEvent,
} from "react";

import { TBody, Td, Th, THead, Tr } from "@/components/display/table";
import type { AnimationProp } from "@/lib/motion";
import { useTweened } from "@/lib/motion/react";
import { cn } from "@/lib/utils/cn";
import { ChartLegend } from "../chart-legend";
import { radiusFor, shapePath } from "../_kernel/encode";
import { formatExact } from "../_kernel/format";
import {
  edgePath,
  graphTarget,
  hullAround,
  liveEdges,
  neighbours,
  type GraphEdge,
  type GraphLayout,
  type GraphNode,
  type Point,
} from "../_kernel/graph";
import { px } from "../_kernel/scale";
import { categoryColor, seriesShape } from "../_kernel/scatter";
import { ChartData } from "../_shared/chart-data";
import chart from "../_shared/chart.module.css";
import { useChartMotion } from "../_shared/use-chart-motion";
import styles from "./network-graph.module.css";

export type { GraphEdge, GraphLayout, GraphNode };

export type NetworkGraphProps = {
  /** Names the chart. */
  label: string;
  nodes: readonly GraphNode[];
  edges: readonly GraphEdge[];
  /** How position is decided — and so what it means. */
  layout?: GraphLayout;
  /** The centre of a radial layout. */
  root?: string;
  /** Groups in a FIXED order: colour, shape, and the tiers of a tiered
   *  layout. */
  groups?: readonly string[];
  /** Bow edges into arcs, where straight chords would overlap. */
  curved?: boolean;
  /** Print node names; off for dense graphs where they would be a wash. */
  labels?: boolean;
  /** Labelled regions drawn behind groups of nodes. */
  hulls?: readonly { key: string; label?: string; ids: readonly string[] }[];
  /** Makes nodes selectable: one tab stop, arrow keys move between nodes. */
  onSelect?: (id: string | null) => void;
  selected?: string | null;
  /** Width over height. */
  aspect?: number;
  formatValue?: (value: number) => string;
  /** Default: nodes pop in; changing the layout glides them to their new
   *  places. */
  animation?: AnimationProp;
  className?: string;
};

/** Things and the connections between them. What position means depends
 *  on the layout — a force layout's nearness is a hint, a radial ring is a
 *  hop count — so choose the layout for the question. Hover or focus a node
 *  to light its neighbours; the tables list every node and connection. */
export function NetworkGraph({
  label,
  nodes,
  edges: rawEdges,
  layout = "force",
  root,
  groups: groupOrder,
  curved = false,
  labels = true,
  hulls = [],
  onSelect,
  selected = null,
  aspect = 1.6,
  formatValue = formatExact,
  animation,
  className,
}: NetworkGraphProps) {
  const { rootProps, update } = useChartMotion(animation, {
    enter: "pop",
    axis: "y",
  });
  const edges = useMemo(() => liveEdges(nodes, rawEdges), [nodes, rawEdges]);
  const groups = useMemo(
    () =>
      groupOrder ??
      [...new Set(nodes.map((n) => n.group ?? ""))].filter(Boolean),
    [groupOrder, nodes],
  );
  // The layout is computed once per input, not per hover or tween frame.
  const target = useMemo(
    () =>
      graphTarget(nodes, edges, layout, aspect, {
        root,
        groups,
        // With hulls the groups are the point, so the force layout gathers
        // each into its own region.
        cluster: hulls.length > 0,
      }),
    [nodes, edges, layout, aspect, root, groups, hulls.length],
  );
  const shown = useTweened(target, update, "target");
  const near = useMemo(() => neighbours(nodes, edges), [nodes, edges]);

  const [pointed, setPointed] = useState<string | null>(null);
  const [active, setActive] = useState(0);
  const svg = useRef<SVGSVGElement>(null);
  const lit = pointed ?? selected;
  const stateOf = (id: string) =>
    lit === null
      ? undefined
      : id === lit
        ? "lit"
        : near.get(lit)?.has(id)
          ? "near"
          : "dim";

  // The frame fits the laid-out nodes, with room for their labels.
  const at = (id: string): Point | null => {
    const x = shown[`${id}|x`];
    const y = shown[`${id}|y`];
    return x === undefined || y === undefined ? null : { x, y };
  };
  const finals = nodes.flatMap((n) => {
    const x = target[`${n.id}|x`];
    const y = target[`${n.id}|y`];
    return x === undefined ? [] : [{ x, y }];
  });
  const left = Math.min(0, ...finals.map((p) => p.x)) - 60;
  const right = Math.max(1000, ...finals.map((p) => p.x)) + 60;
  const top = Math.min(0, ...finals.map((p) => p.y)) - 50;
  const bottom = Math.max(1000 / aspect, ...finals.map((p) => p.y)) + 50;
  const width = right - left;
  const height = bottom - top;
  const pct = (p: Point) => ({
    left: `${((p.x - left) / width) * 100}%`,
    top: `${((p.y - top) / height) * 100}%`,
  });

  const sizes = nodes
    .map((n) => n.size)
    .filter((s): s is number => typeof s === "number" && s > 0);
  const range: [number, number] = sizes.length
    ? [Math.min(...sizes), Math.max(...sizes)]
    : [1, 1];
  const radius = (n: GraphNode) =>
    n.size && n.size > 0 ? radiusFor(n.size, range, [9, 26]) : 11;
  const maxWeight = Math.max(1, ...edges.map((e) => e.weight ?? 0));
  const degree = (id: string) => near.get(id)?.size ?? 0;

  const select = (id: string) => onSelect?.(selected === id ? null : id);
  const move = (event: KeyboardEvent) => {
    if (!onSelect) return;
    const step = { ArrowRight: 1, ArrowDown: 1, ArrowLeft: -1, ArrowUp: -1 }[
      event.key
    ];
    if (event.key === "Escape") {
      onSelect(null);
      return;
    }
    if (step === undefined) return;
    event.preventDefault();
    const next = (active + step + nodes.length) % nodes.length;
    setActive(next);
    svg.current?.querySelector<SVGGElement>(`[data-index="${next}"]`)?.focus();
  };

  if (!nodes.length)
    return (
      <div className={cn(chart.root, className)}>
        <p className={chart.empty}>No data to display.</p>
      </div>
    );

  return (
    <div {...rootProps} className={cn(chart.root, className)}>
      {groups.length > 1 ? (
        <ChartLegend
          items={groups.map((group) => ({
            key: group,
            label: group,
            color: categoryColor(groups, group),
            shape: seriesShape(groups, group),
          }))}
        />
      ) : null}
      <div
        className={styles.frame}
        style={{ "--aspect": width / height } as CSSProperties}
      >
        <svg
          ref={svg}
          className={styles.svg}
          viewBox={`${px(left)} ${px(top)} ${px(width)} ${px(height)}`}
          role={onSelect ? "group" : "img"}
          aria-label={`${label}. Every node and connection is in the data tables.`}
          data-lit={lit ? "" : undefined}
          onKeyDown={onSelect ? move : undefined}
        >
          {hulls.map((hull, index) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape ? (
              <ellipse
                key={hull.key}
                className={styles.hull}
                style={
                  {
                    "--series": categoryColor(
                      hulls.map((h) => h.key),
                      hulls[index].key,
                    ),
                  } as CSSProperties
                }
                cx={shape.cx}
                cy={shape.cy}
                rx={shape.rx}
                ry={shape.ry}
              />
            ) : null;
          })}
          {edges.map((edge, index) => {
            const a = at(edge.from);
            const b = at(edge.to);
            if (!a || !b) return null;
            const signed = typeof edge.value === "number";
            return (
              <path
                key={`${edge.from}-${edge.to}-${index}`}
                className={styles.edge}
                d={edgePath(a, b, curved)}
                data-lit={
                  lit !== null && (edge.from === lit || edge.to === lit)
                    ? ""
                    : undefined
                }
                data-sign={
                  signed
                    ? (edge.value as number) < 0
                      ? "negative"
                      : "positive"
                    : undefined
                }
                style={
                  {
                    "--edge-w": 1 + ((edge.weight ?? 0) / maxWeight) * 3,
                    "--edge-o": signed
                      ? 0.25 +
                        Math.min(1, Math.abs(edge.value as number)) * 0.65
                      : undefined,
                  } as CSSProperties
                }
              />
            );
          })}
          {nodes.map((node, index) => {
            const p = at(node.id);
            if (!p) return null;
            const r = radius(node);
            const name = node.label ?? node.id;
            return (
              <g key={node.id} transform={`translate(${px(p.x)} ${px(p.y)})`}>
                <g
                  data-mark
                  data-index={index}
                  data-state={stateOf(node.id)}
                  className={styles.node}
                  style={
                    {
                      "--series": categoryColor(groups, node.group),
                    } as CSSProperties
                  }
                  onPointerEnter={() => setPointed(node.id)}
                  onPointerLeave={() => setPointed(null)}
                  onFocus={() => {
                    setPointed(node.id);
                    setActive(index);
                  }}
                  onBlur={() => setPointed(null)}
                  {...(onSelect
                    ? {
                        role: "button",
                        tabIndex: index === active ? 0 : -1,
                        "aria-label": `${name}${node.group ? `, ${node.group}` : ""}, ${degree(node.id)} connections`,
                        "aria-pressed": selected === node.id,
                        onClick: () => select(node.id),
                        onKeyDown: (event: KeyboardEvent) => {
                          if (event.key === "Enter" || event.key === " ") {
                            event.preventDefault();
                            select(node.id);
                          }
                        },
                      }
                    : {})}
                >
                  <circle className={styles.ring} r={r + 5} />
                  <path
                    className={styles.shape}
                    d={shapePath(seriesShape(groups, node.group), r)}
                  />
                </g>
              </g>
            );
          })}
        </svg>
        <div className={styles.labels} aria-hidden="true">
          {hulls.map((hull) => {
            const shape = hullAround(hull.ids.flatMap((id) => at(id) ?? []));
            return shape && hull.label ? (
              <span
                key={hull.key}
                data-hull
                style={pct({ x: shape.cx, y: shape.cy - shape.ry })}
              >
                {hull.label}
              </span>
            ) : null;
          })}
          {labels
            ? nodes.map((node) => {
                const p = at(node.id);
                return p ? (
                  <span
                    key={node.id}
                    data-state={stateOf(node.id)}
                    style={pct({ x: p.x, y: p.y + radius(node) })}
                  >
                    {node.label ?? node.id}
                  </span>
                ) : null;
              })
            : null}
        </div>
      </div>
      <ChartData label={label} summary="View nodes">
        <THead>
          <Tr>
            <Th>Node</Th>
            <Th>Group</Th>
            <Th numeric>Connections</Th>
            {sizes.length ? <Th numeric>Size</Th> : null}
          </Tr>
        </THead>
        <TBody>
          {nodes.map((node) => (
            <Tr key={node.id}>
              <Th scope="row">{node.label ?? node.id}</Th>
              <Td>{node.group ?? "—"}</Td>
              <Td numeric>{degree(node.id)}</Td>
              {sizes.length ? (
                <Td numeric>
                  {typeof node.size === "number" ? formatValue(node.size) : "—"}
                </Td>
              ) : null}
            </Tr>
          ))}
        </TBody>
      </ChartData>
      <ChartData label={label} summary="View connections">
        <THead>
          <Tr>
            <Th>From</Th>
            <Th>To</Th>
            <Th numeric>Value</Th>
          </Tr>
        </THead>
        <TBody>
          {edges.map((edge, index) => {
            const name = (id: string) =>
              nodes.find((n) => n.id === id)?.label ?? id;
            const value = edge.value ?? edge.weight;
            return (
              <Tr key={index}>
                <Th scope="row">{name(edge.from)}</Th>
                <Td>{name(edge.to)}</Td>
                <Td numeric>
                  {typeof value === "number" ? formatValue(value) : "—"}
                </Td>
              </Tr>
            );
          })}
        </TBody>
      </ChartData>
    </div>
  );
}

components/charts/network-graph/network-graph.module.css

@layer primitive {
  .frame {
    position: relative;
    width: 100%;
    aspect-ratio: var(--aspect, 1.6);
  }
  .svg {
    position: absolute;
    inset: 0;
    width: 100%;
    height: 100%;
    overflow: visible;
  }
  .hull {
    fill: color-mix(in oklab, var(--series) 12%, transparent);
    stroke: color-mix(in oklab, var(--series) 45%, transparent);
    stroke-dasharray: 4 4;
    stroke-width: 1;
    vector-effect: non-scaling-stroke;
  }
  .edge {
    fill: none;
    stroke: var(--chart-axis, var(--line-strong));
    stroke-opacity: 0.7;
    stroke-width: var(--edge-w, 1.25);
    vector-effect: non-scaling-stroke;
    transition: stroke-opacity var(--dur-2) var(--ease);
  }
  .edge[data-sign="positive"] {
    stroke: var(--chart-pos);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .edge[data-sign="negative"] {
    stroke: var(--chart-neg);
    stroke-opacity: var(--edge-o, 0.7);
  }
  .svg[data-lit] .edge:not([data-lit]) {
    stroke-opacity: 0.12;
  }
  .node {
    transform-origin: center;
    transition: opacity var(--dur-2) var(--ease);
  }
  .shape {
    fill: var(--series);
    stroke: var(--surface-panel);
    stroke-width: 1.5;
    vector-effect: non-scaling-stroke;
  }
  .svg[data-lit] .node[data-state="dim"] {
    opacity: 0.25;
  }
  .ring {
    fill: none;
    stroke: var(--accent);
    stroke-width: 2.5;
    vector-effect: non-scaling-stroke;
    opacity: 0;
  }
  .node[data-state="lit"] .ring,
  .node[aria-pressed="true"] .ring {
    opacity: 1;
  }
  .node[role="button"] {
    cursor: pointer;
    outline: none;
  }
  .node[role="button"]:focus-visible .ring {
    stroke-dasharray: 3 2;
    opacity: 1;
  }
  .labels {
    position: absolute;
    inset: 0;
    pointer-events: none;
    font-size: var(--text-11);
  }
  .labels span {
    position: absolute;
    color: var(--ink-2);
    white-space: nowrap;
    transform: translate(-50%, 6px);
    transition: opacity var(--dur-2) var(--ease);
  }
  .labels span[data-state="dim"] {
    opacity: 0.25;
  }
  .labels span[data-hull] {
    color: var(--ink-3);
    font-weight: var(--weight-medium);
    transform: translate(-50%, -100%);
  }
}

components/charts/_kernel/graph.ts

import {
  forceCollide,
  forceLink,
  forceManyBody,
  forceSimulation,
  forceX,
  forceY,
  type SimulationNodeDatum,
} from "d3-force";

import { px } from "./scale";

/* NetworkGraph's maths: layouts and geometry, all deterministic, so the
   server and the browser draw the same picture.

   A force layout is chaotic: a one-bit difference in step one grows into a
   visibly different graph. ECMAScript leaves cos, sin, hypot, exp, and log
   to each engine, so none of them appear inside the simulation — starting
   positions come from a hash, the simulation's randomness from a seeded
   generator, and distances from sqrt, which IEEE-754 specifies exactly. */

export type GraphNode = {
  id: string;
  label?: string;
  /** A class: sets colour and shape (by `groups` order), and the tier in a
   *  tiered layout. */
  group?: string;
  /** A magnitude drawn as the node's area. */
  size?: number;
};

export type GraphEdge = {
  from: string;
  to: string;
  /** Signed, −1 to 1: hue is the sign, opacity the strength. */
  value?: number;
  /** Unsigned strength: drawn as width. */
  weight?: number;
  label?: string;
};

export type GraphLayout =
  "force" | "radial" | "circular" | "tiered" | "flow" | "grid";
export type Point = { x: number; y: number };

/** The virtual canvas layouts place nodes on. */
export const GRAPH_W = 1000;

/** FNV-1a → 0–1: a repeatable number per string. */
export function seedOf(text: string) {
  let h = 2166136261;
  for (let i = 0; i < text.length; i++) {
    h ^= text.charCodeAt(i);
    h = Math.imul(h, 16777619);
  }
  return (h >>> 0) / 4294967296;
}

/** A seeded linear congruential generator for the simulation's jiggle. */
function lcg(seed: number) {
  let s = Math.floor(seed * 4294967296) >>> 0 || 1;
  return () => {
    s = (Math.imul(1664525, s) + 1013904223) >>> 0;
    return s / 4294967296;
  };
}

/** Edges whose ends both exist; a dangling edge is ignored, not guessed. */
export function liveEdges(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const ids = new Set(nodes.map((n) => n.id));
  return edges.filter(
    (e) => ids.has(e.from) && ids.has(e.to) && e.from !== e.to,
  );
}

export function neighbours(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
) {
  const near = new Map<string, Set<string>>(
    nodes.map((n) => [n.id, new Set()]),
  );
  for (const e of edges) {
    near.get(e.from)?.add(e.to);
    near.get(e.to)?.add(e.from);
  }
  return near;
}

/** Hops from a root, walking edges both ways; unreached nodes go one ring
 *  beyond the furthest. */
export function hopsFrom(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  root: string,
) {
  const near = neighbours(nodes, edges);
  const depth = new Map<string, number>([[root, 0]]);
  let frontier = [root];
  while (frontier.length) {
    const next: string[] = [];
    for (const id of frontier)
      for (const other of near.get(id) ?? []) {
        if (depth.has(other)) continue;
        depth.set(other, (depth.get(id) ?? 0) + 1);
        next.push(other);
      }
    frontier = next;
  }
  const beyond = Math.max(0, ...depth.values()) + 1;
  for (const n of nodes) if (!depth.has(n.id)) depth.set(n.id, beyond);
  return depth;
}

/** Split edges into those that keep the graph acyclic and the "back"
 *  edges that close a loop, by depth-first search in input order: a loop is
 *  broken at the edge that closes it (c → a in a → b → c → a), not wherever
 *  a walk happens to land. */
export function splitLoops<E extends { from: string; to: string }>(
  nodes: readonly { id: string }[],
  edges: readonly E[],
) {
  const outgoing = new Map<string, E[]>(nodes.map((n) => [n.id, []]));
  for (const e of edges) outgoing.get(e.from)?.push(e);
  const state = new Map<string, 1 | 2>();
  const back = new Set<E>();
  const visit = (id: string) => {
    state.set(id, 1);
    for (const e of outgoing.get(id) ?? []) {
      const s = state.get(e.to);
      if (s === 1) back.add(e);
      else if (s === undefined) visit(e.to);
    }
    state.set(id, 2);
  };
  for (const n of nodes) if (!state.has(n.id)) visit(n.id);
  return {
    forward: edges.filter((e) => !back.has(e)),
    loops: edges.filter((e) => back.has(e)),
  };
}

/** Longest path from any source, for flow layouts; loops are broken first
 *  (see splitLoops). */
export function longestPath(
  nodes: readonly { id: string }[],
  edges: readonly { from: string; to: string }[],
) {
  const { forward } = splitLoops(nodes, edges);
  const incoming = new Map<string, string[]>(nodes.map((n) => [n.id, []]));
  for (const e of forward) incoming.get(e.to)?.push(e.from);
  const depth = new Map<string, number>();
  const walk = (id: string): number => {
    const known = depth.get(id);
    if (known !== undefined) return known;
    const from = incoming.get(id) ?? [];
    const d = from.length ? Math.max(...from.map((f) => walk(f) + 1)) : 0;
    depth.set(id, d);
    return d;
  };
  for (const n of nodes) walk(n.id);
  return depth;
}

type Options = { root?: string; groups: readonly string[]; cluster?: boolean };

type Layout = (
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  height: number,
  options: Options,
) => Map<string, Point>;

/** Where each group gathers when a force layout is clustered, as fractions
 *  of the canvas. A fixed table, not points on a circle: anything that feeds
 *  the simulation must avoid engine-dependent maths. */
const ANCHORS: readonly (readonly [number, number])[][] = [
  [[0.5, 0.5]],
  [
    [0.28, 0.5],
    [0.72, 0.5],
  ],
  [
    [0.5, 0.26],
    [0.26, 0.72],
    [0.74, 0.72],
  ],
  [
    [0.28, 0.28],
    [0.72, 0.28],
    [0.28, 0.72],
    [0.72, 0.72],
  ],
  [
    [0.5, 0.2],
    [0.2, 0.45],
    [0.8, 0.45],
    [0.32, 0.8],
    [0.68, 0.8],
  ],
];

const force: Layout = (nodes, edges, height, { groups, cluster }) => {
  type Sim = SimulationNodeDatum & { id: string };
  const sim: Sim[] = nodes.map((n) => ({
    id: n.id,
    x: GRAPH_W * (0.25 + seedOf(`${n.id}:x`) * 0.5),
    y: height * (0.25 + seedOf(`${n.id}:y`) * 0.5),
  }));
  const spacing = Math.sqrt((GRAPH_W * height) / Math.max(1, nodes.length));
  const simulation = forceSimulation(sim)
    .randomSource(lcg(seedOf(nodes.map((n) => n.id).join("|"))))
    .force(
      "link",
      forceLink<Sim, { source: string; target: string }>(
        edges.map((e) => ({ source: e.from, target: e.to })),
      )
        .id((d) => d.id)
        .distance(spacing * 0.55),
    )
    .force("charge", forceManyBody().strength(-spacing * 2))
    .force("collide", forceCollide(24))
    .stop();
  // Clustered, each group is drawn toward its own region (up to five
  // groups); otherwise everything is drawn gently toward the centre.
  const table = ANCHORS[Math.min(groups.length, ANCHORS.length) - 1];
  const groupOf = new Map(nodes.map((n) => [n.id, n.group ?? ""]));
  const anchor = (id: string) => {
    const index = groups.indexOf(groupOf.get(id) ?? "");
    return cluster && table && index >= 0 && index < table.length
      ? table[index]
      : [0.5, 0.5];
  };
  const pull = cluster ? 0.18 : 0.06;
  simulation
    .force("x", forceX<Sim>((d) => anchor(d.id)[0] * GRAPH_W).strength(pull))
    .force(
      "y",
      forceY<Sim>((d) => anchor(d.id)[1] * height).strength(
        pull * (GRAPH_W / height),
      ),
    );
  simulation.tick(300);
  return fit(
    new Map(sim.map((n) => [n.id, { x: n.x ?? 0, y: n.y ?? 0 }])),
    height,
  );
};

/** Scale positions uniformly (so shapes keep their proportions) to fill the
 *  canvas, less a margin for labels. */
function fit(points: Map<string, Point>, height: number, margin = 70) {
  if (points.size < 2)
    return new Map(
      [...points].map(([id]) => [id, { x: GRAPH_W / 2, y: height / 2 }]),
    );
  const xs = [...points.values()].map((p) => p.x);
  const ys = [...points.values()].map((p) => p.y);
  const [x0, x1, y0, y1] = [
    Math.min(...xs),
    Math.max(...xs),
    Math.min(...ys),
    Math.max(...ys),
  ];
  const scale = Math.min(
    (GRAPH_W - 2 * margin) / Math.max(1, x1 - x0),
    (height - 2 * margin) / Math.max(1, y1 - y0),
  );
  const ox = (GRAPH_W - (x1 - x0) * scale) / 2;
  const oy = (height - (y1 - y0) * scale) / 2;
  return new Map(
    [...points].map(([id, p]) => [
      id,
      { x: px(ox + (p.x - x0) * scale), y: px(oy + (p.y - y0) * scale) },
    ]),
  );
}

const circle = (
  count: number,
  index: number,
  cx: number,
  cy: number,
  r: number,
  turn = 0,
) => {
  const angle = (index / Math.max(1, count)) * 2 * Math.PI - Math.PI / 2 + turn;
  return { x: px(cx + r * Math.cos(angle)), y: px(cy + r * Math.sin(angle)) };
};

const radial: Layout = (nodes, edges, height, { root }) => {
  const centre = root ?? nodes[0]?.id ?? "";
  const depth = hopsFrom(nodes, edges, centre);
  const near = neighbours(nodes, edges);
  const rings = new Map<number, string[]>();
  for (const n of nodes) {
    if (n.id === centre) continue;
    const d = depth.get(n.id) ?? 1;
    rings.set(d, [...(rings.get(d) ?? []), n.id]);
  }
  const out = new Map<string, Point>([
    [centre, { x: GRAPH_W / 2, y: height / 2 }],
  ]);
  // Turns around the centre, per node, so a ring can follow the one inside.
  const turn = new Map<string, number>([[centre, 0]]);
  const count = Math.max(1, rings.size);
  const outer = Math.min(GRAPH_W, height) / 2 - 50;
  for (const [ring, ids] of [...rings].sort((a, b) => a[0] - b[0])) {
    // Order a ring by where its parent sits, so children stay beside their
    // parent and edges do not cross the middle.
    const parentTurn = (id: string) => {
      const parents = [...(near.get(id) ?? [])].filter(
        (p) => turn.has(p) && (depth.get(p) ?? 0) < ring,
      );
      return parents.length ? Math.min(...parents.map((p) => turn.get(p)!)) : 1;
    };
    const ordered = [...ids].sort(
      (a, b) => parentTurn(a) - parentTurn(b) || a.localeCompare(b),
    );
    const r = (outer * ring) / count;
    ordered.forEach((id, i) => {
      const t = (i + 0.5) / ordered.length;
      turn.set(id, t);
      out.set(id, circle(1, 0, GRAPH_W / 2, height / 2, r, t * 2 * Math.PI));
    });
  }
  return out;
};

const circular: Layout = (nodes, _edges, height) => {
  const r = Math.min(GRAPH_W, height) / 2 - 40;
  return new Map(
    nodes.map((n, i) => [
      n.id,
      circle(nodes.length, i, GRAPH_W / 2, height / 2, r),
    ]),
  );
};

const tiered: Layout = (nodes, _edges, height, { groups }) => {
  const order = [
    ...new Set([...groups, ...nodes.map((n) => n.group ?? "")]),
  ].filter((g) => nodes.some((n) => (n.group ?? "") === g));
  const out = new Map<string, Point>();
  order.forEach((group, column) => {
    const ids = nodes.filter((n) => (n.group ?? "") === group).map((n) => n.id);
    const x =
      order.length === 1
        ? GRAPH_W / 2
        : 60 + (column * (GRAPH_W - 120)) / (order.length - 1);
    ids.forEach((id, i) =>
      out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
    );
  });
  return out;
};

const flow: Layout = (nodes, edges, height) => {
  const depth = longestPath(nodes, edges);
  const columns = new Map<number, string[]>();
  for (const n of nodes) {
    const d = depth.get(n.id) ?? 0;
    columns.set(d, [...(columns.get(d) ?? []), n.id]);
  }
  const count = Math.max(1, columns.size);
  const out = new Map<string, Point>();
  [...columns]
    .sort((a, b) => a[0] - b[0])
    .forEach(([, ids], column) => {
      const x =
        count === 1
          ? GRAPH_W / 2
          : 60 + (column * (GRAPH_W - 120)) / (count - 1);
      ids.forEach((id, i) =>
        out.set(id, { x: px(x), y: px(((i + 1) * height) / (ids.length + 1)) }),
      );
    });
  return out;
};

const grid: Layout = (nodes, _edges, height) => {
  const cols = Math.max(
    1,
    Math.ceil(Math.sqrt(nodes.length * (GRAPH_W / height))),
  );
  const rows = Math.max(1, Math.ceil(nodes.length / cols));
  return new Map(
    nodes.map((n, i) => [
      n.id,
      {
        x: px((((i % cols) + 1) * GRAPH_W) / (cols + 1)),
        y: px(((Math.floor(i / cols) + 1) * height) / (rows + 1)),
      },
    ]),
  );
};

const LAYOUTS: Record<GraphLayout, Layout> = {
  force,
  radial,
  circular,
  tiered,
  flow,
  grid,
};

/** Every node's position, as a record for tweening: `${id}|x`, `${id}|y`. */
export function graphTarget(
  nodes: readonly GraphNode[],
  edges: readonly GraphEdge[],
  layout: GraphLayout,
  aspect: number,
  options: Options,
) {
  const height = GRAPH_W / aspect;
  const placed = nodes.length
    ? LAYOUTS[layout](nodes, edges, height, options)
    : new Map();
  const target: Record<string, number> = {};
  for (const [id, p] of placed) {
    target[`${id}|x`] = p.x;
    target[`${id}|y`] = p.y;
  }
  return target;
}

/** A straight edge, or a shallow arc that bows with length — straight for
 *  radial layouts, arcs where chords would overlap into a disc. */
export function edgePath(a: Point, b: Point, curved: boolean) {
  if (!curved) return `M${px(a.x)},${px(a.y)}L${px(b.x)},${px(b.y)}`;
  const dx = b.x - a.x;
  const dy = b.y - a.y;
  const distance = Math.sqrt(dx * dx + dy * dy) || 1;
  const bow = Math.min(distance * 0.18, 60);
  const mx = (a.x + b.x) / 2 - (dy / distance) * bow;
  const my = (a.y + b.y) / 2 + (dx / distance) * bow;
  return `M${px(a.x)},${px(a.y)}Q${px(mx)},${px(my)} ${px(b.x)},${px(b.y)}`;
}

/** An ellipse around a set of positions, for a labelled group (a hull). */
export function hullAround(points: readonly Point[]) {
  if (!points.length) return null;
  const cx = points.reduce((sum, p) => sum + p.x, 0) / points.length;
  const cy = points.reduce((sum, p) => sum + p.y, 0) / points.length;
  const r =
    Math.max(
      34,
      ...points.map((p) => {
        const dx = p.x - cx;
        const dy = p.y - cy;
        return Math.sqrt(dx * dx + dy * dy);
      }),
    ) + 30;
  return { cx: px(cx), cy: px(cy), rx: px(r * 1.12), ry: px(r) };
}

components/charts/sankey-chart/doc.ts

/**
 * SankeyChart — quantities flowing through stages.
 *
 * ┌───────────────────────────────────────────────────────────────────────────┐
 * │ § CONTRACT — the oracle. Names no library, contains no code.              │
 * └───────────────────────────────────────────────────────────────────────────┘
 *
 * # Shape
 *
 *     label         REQUIRED
 *     nodes         { id, label }[]
 *     links         { from, to, value: number | null }[]
 *     aspect?, formatValue?, animation?  (default: flows wipe in)
 *
 * # Behaviour
 *
 * R1  Stages come from the links: a node sits one column after the furthest
 *     node that feeds it.
 * R2  Ribbon width is the quantity, on one scale for the whole chart; a
 *     node is as tall as the larger of what enters and what leaves it.
 * R3  A downstream node takes the colour of its largest source, so a flow
 *     keeps its colour across the chart.
 * R4  A link that would close a loop is not drawn (never backwards); the
 *     table reports it. A null, zero, or negative link is not drawn.
 * R5  Every node is labelled with its throughput; the table lists every
 *     link.
 */
export {};

components/charts/sankey-chart/sankey-chart.tsx

"use client";

import { useState, type CSSProperties } from "react";

import { TBody, Td, Th, THead, Tr } from "@/components/display/table";
import type { AnimationProp } from "@/lib/motion";
import { useTweened } from "@/lib/motion/react";
import { cn } from "@/lib/utils/cn";
import { formatExact } from "../_kernel/format";
import {
  sankeyLayout,
  sankeyLinks,
  sankeyTarget,
  type SankeyLink,
  type SankeyNode,
} from "../_kernel/sankey";
import { isValue, px } from "../_kernel/scale";
import { ChartData } from "../_shared/chart-data";
import chart from "../_shared/chart.module.css";
import { useChartMotion } from "../_shared/use-chart-motion";
import styles from "./sankey-chart.module.css";

export type { SankeyLink, SankeyNode };

export type SankeyChartProps = {
  /** Names the chart. */
  label: string;
  nodes: readonly SankeyNode[];
  /** Quantities from one node to another. Stages are worked out from the
   *  links: a node sits one column after the furthest node that feeds it. */
  links: readonly SankeyLink[];
  /** Width over height. */
  aspect?: number;
  formatValue?: (value: number) => string;
  /** Default: flows wipe in from the left, when scrolled into view. */
  animation?: AnimationProp;
  className?: string;
};

/** Quantities flowing through stages: where signups come from, which plan
 *  they pick, whether they stay. Ribbon width is the quantity, on one scale
 *  for the whole chart. Hover a node to light its flows. */
export function SankeyChart({
  label,
  nodes,
  links,
  aspect = 2,
  formatValue = formatExact,
  animation,
  className,
}: SankeyChartProps) {
  const { rootProps, update } = useChartMotion(animation, {
    enter: "wipe",
    axis: "x",
  });
  const shown = useTweened(sankeyTarget(links), update);
  const [lit, setLit] = useState<string | null>(null);
  const W = 1000;
  const H = W / aspect;
  const layout = sankeyLayout(nodes, links, shown, W, H);
  const { loops } = sankeyLinks(nodes, links);
  const name = (id: string) => nodes.find((n) => n.id === id)?.label ?? id;
  const pct = (x: number, y: number) => ({
    left: `${(x / W) * 100}%`,
    top: `${(y / H) * 100}%`,
  });

  if (!nodes.length || !layout.links.length)
    return (
      <div className={cn(chart.root, className)}>
        <p className={chart.empty}>
          {nodes.length ? "Measurements unavailable." : "No data to display."}
        </p>
      </div>
    );

  return (
    <div {...rootProps} className={cn(chart.root, className)}>
      <div
        className={styles.frame}
        style={{ "--aspect": aspect } as CSSProperties}
      >
        <svg
          className={styles.svg}
          viewBox={`0 0 ${W} ${px(H)}`}
          preserveAspectRatio="none"
          role="img"
          aria-label={`${label}. Every flow is in the data table.`}
          data-lit={lit ? "" : undefined}
        >
          {layout.links.map((link) => (
            <path
              key={link.key}
              data-mark
              data-lit={
                lit !== null && (link.from === lit || link.to === lit)
                  ? ""
                  : undefined
              }
              className={styles.link}
              d={link.path}
              strokeWidth={Math.max(1, link.width)}
              style={{ "--series": link.color } as CSSProperties}
            />
          ))}
          {layout.nodes.map((node) =>
            node.value > 0 ? (
              <rect
                key={node.id}
                data-mark
                className={styles.node}
                x={px(node.x)}
                y={px(node.y)}
                width={layout.nodeWidth}
                height={px(Math.max(1, node.height))}
                style={{ "--series": node.color } as CSSProperties}
                onPointerEnter={() => setLit(node.id)}
                onPointerLeave={() => setLit(null)}
              />
            ) : null,
          )}
        </svg>
        <div className={styles.labels} aria-hidden="true">
          {layout.nodes.map((node) => {
            if (node.value <= 0) return null;
            const last =
              node.column === layout.columns - 1 && layout.columns > 1;
            return (
              <span
                key={node.id}
                data-side={last ? "left" : "right"}
                style={pct(
                  last ? node.x : node.x + layout.nodeWidth,
                  node.y + node.height / 2,
                )}
              >
                {node.label}
                <b>{formatValue(node.value)}</b>
              </span>
            );
          })}
        </div>
      </div>
      <ChartData label={label}>
        <THead>
          <Tr>
            <Th>From</Th>
            <Th>To</Th>
            <Th numeric>Value</Th>
          </Tr>
        </THead>
        <TBody>
          {links.map((link, index) => {
            const loop = loops.includes(link);
            return (
              <Tr key={index}>
                <Th scope="row">{name(link.from)}</Th>
                <Td>{name(link.to)}</Td>
                <Td numeric>
                  {isValue(link.value)
                    ? `${formatValue(link.value)}${loop ? " (not drawn: it forms a loop)" : ""}`
                    : "Unavailable"}
                </Td>
              </Tr>
            );
          })}
        </TBody>
      </ChartData>
    </div>
  );
}

components/charts/_kernel/sankey.ts

import { colorVar, type ChartColor } from "./encode";
import { longestPath, splitLoops } from "./graph";
import { isValue, px } from "./scale";

/* SankeyChart: quantities flowing through stages. */

export type SankeyNode = { id: string; label: string };
export type SankeyLink = { from: string; to: string; value: number | null };

export type SankeyLayoutNode = SankeyNode & {
  column: number;
  x: number;
  y: number;
  height: number;
  value: number;
  inflow: number;
  outflow: number;
  color: string;
};

export type SankeyLayoutLink = {
  key: string;
  from: string;
  to: string;
  value: number;
  width: number;
  path: string;
  color: string;
};

const linkKey = (l: { from: string; to: string }) => `${l.from}>${l.to}`;

/** The links that can be drawn: both ends exist, the value is finite and
 *  positive, and it runs forward. A link that would close a loop is kept
 *  out of the picture (and reported), never drawn backwards. */
export function sankeyLinks(
  nodes: readonly SankeyNode[],
  links: readonly SankeyLink[],
) {
  const ids = new Set(nodes.map((n) => n.id));
  const candidate = links.filter(
    (l) =>
      ids.has(l.from) &&
      ids.has(l.to) &&
      l.from !== l.to &&
      isValue(l.value) &&
      l.value > 0,
  );
  const { forward, loops } = splitLoops(nodes, candidate);
  const depth = longestPath(nodes, forward);
  return { forward, loops, depth };
}

export function sankeyTarget(links: readonly SankeyLink[]) {
  const target: Record<string, number> = {};
  for (const l of links)
    if (isValue(l.value) && l.value > 0) target[linkKey(l)] = l.value;
  return target;
}

/** Positions for the tweened link values, in a `width` × `height` space. */
export function sankeyLayout(
  nodes: readonly SankeyNode[],
  links: readonly SankeyLink[],
  shown: Readonly<Record<string, number>>,
  width: number,
  height: number,
  { nodeWidth = 14, gap = 14 } = {},
) {
  const { forward, depth } = sankeyLinks(nodes, links);
  const flows = forward.map((l) => ({ ...l, value: shown[linkKey(l)] ?? 0 }));
  const columns = Math.max(0, ...nodes.map((n) => depth.get(n.id) ?? 0)) + 1;

  const placed = new Map<string, SankeyLayoutNode>();
  nodes.forEach((node, index) => {
    const inflow = flows
      .filter((l) => l.to === node.id)
      .reduce((s, l) => s + l.value, 0);
    const outflow = flows
      .filter((l) => l.from === node.id)
      .reduce((s, l) => s + l.value, 0);
    const column = depth.get(node.id) ?? 0;
    placed.set(node.id, {
      ...node,
      column,
      x:
        columns === 1
          ? width / 2
          : (column * (width - nodeWidth)) / (columns - 1),
      y: 0,
      height: 0,
      value: Math.max(inflow, outflow),
      inflow,
      outflow,
      color: colorVar(((index % 4) + 1) as ChartColor),
    });
  });

  // One vertical scale for every column: the fullest column fills the height.
  const byColumn = Array.from({ length: columns }, (_, c) =>
    [...placed.values()].filter((n) => n.column === c && n.value > 0),
  );
  const scale = Math.min(
    ...byColumn
      .filter((c) => c.length)
      .map(
        (c) =>
          (height - gap * (c.length - 1)) / c.reduce((s, n) => s + n.value, 0),
      ),
  );
  for (const column of byColumn) {
    const used =
      column.reduce((s, n) => s + n.value * scale, 0) +
      gap * (column.length - 1);
    let y = (height - used) / 2;
    for (const n of column) {
      n.y = y;
      n.height = n.value * scale;
      y += n.height + gap;
    }
  }

  // First-column nodes keep their hue; everything downstream takes the hue of
  // its largest source, so a flow keeps its colour across the chart.
  for (let c = 1; c < columns; c++)
    for (const n of byColumn[c]) {
      const main = flows
        .filter((l) => l.to === n.id)
        .sort((a, b) => b.value - a.value)[0];
      if (main) n.color = placed.get(main.from)!.color;
    }

  // Links leave a node ordered by where they arrive, and arrive ordered by
  // where they left, so ribbons cross as little as they can.
  const outOffset = new Map<string, number>();
  const inOffset = new Map<string, number>();
  const sorted = [...flows].sort(
    (a, b) =>
      placed.get(a.from)!.y - placed.get(b.from)!.y ||
      placed.get(a.to)!.y - placed.get(b.to)!.y,
  );
  const out: SankeyLayoutLink[] = [];
  const bySource = [...sorted].sort(
    (a, b) => placed.get(a.to)!.y - placed.get(b.to)!.y,
  );
  const sourceY = new Map<string, number>();
  for (const l of bySource) {
    const o = outOffset.get(l.from) ?? 0;
    sourceY.set(linkKey(l), placed.get(l.from)!.y + o);
    outOffset.set(l.from, o + l.value * scale);
  }
  for (const l of sorted) {
    const a = placed.get(l.from)!;
    const b = placed.get(l.to)!;
    const w = l.value * scale;
    const y0 = sourceY.get(linkKey(l))! + w / 2;
    const i = inOffset.get(l.to) ?? 0;
    const y1 = b.y + i + w / 2;
    inOffset.set(l.to, i + w);
    const x0 = a.x + nodeWidth;
    const x1 = b.x;
    const mid = (x0 + x1) / 2;
    out.push({
      key: linkKey(l),
      from: l.from,
      to: l.to,
      value: l.value,
      width: w,
      path: `M${px(x0)},${px(y0)}C${px(mid)},${px(y0)} ${px(mid)},${px(y1)} ${px(x1)},${px(y1)}`,
      color: a.color,
    });
  }
  return { nodes: [...placed.values()], links: out, nodeWidth, columns };
}