# All files / src/utils graphAlgorithms.ts

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     /**
     * @fileoverview Graph algorithms for MEP relationship-network OSINT.
     *
     * Pure, deterministic helpers consumed by `network_analysis`:
     * - {@link buildAdjacency} — adjacency map from a weighted edge list.
     * - {@link bfsLimited} — depth-bounded BFS ego-network extraction.
     * - {@link weightedDegree} — weighted-degree centrality per node.
     * - {@link betweennessCentrality} — Brandes' algorithm (weighted, Dijkstra-based, O(V²·log V) with the current array-backed priority queue).
     * - {@link labelPropagation} — deterministic asynchronous label-propagation community detection.
     * - {@link modularity} — Newman's modularity Q for a partition.
     *
     * Algorithms are deterministic — every iteration orders nodes/edges by string
     * comparison so identical input always produces identical output, satisfying
     * the OSINT reproducibility requirement.
     *
     * ISMS Policy: SC-002 (Input Validation), AC-003 (Least Privilege).
     *
     * @module utils/graphAlgorithms
     * @since 1.4.0
     */

    /** Simple weighted undirected edge representation. */
    export interface WeightedEdge {
      /** Stable identifier of the first endpoint. */
      sourceId: string;
      /** Stable identifier of the second endpoint. */
      targetId: string;
      /** Edge weight in `[0, 1]`. */
      weight: number;
    }

    /** Adjacency representation: `adj.get(node)` → neighbour → weight. */
    export type AdjacencyMap = Map<string, Map<string, number>>;

    /**
     * Build an undirected adjacency map from a weighted edge list.
     *
     * Self-loops are dropped. Parallel edges between the same pair are merged
     * by taking the **maximum** weight (so combined networks remain
     * well-defined when both committee and voting edges describe the same pair).
     *
     * @param nodeIds - Full node universe; nodes without edges still appear as empty maps.
     * @param edges - Weighted edges (order-independent).
     * @returns Adjacency map keyed by node id.
     */
    export function buildAdjacency(nodeIds: readonly string[], edges: readonly WeightedEdge[]): AdjacencyMap {
      const adj: AdjacencyMap = new Map();
      for (const id of nodeIds) adj.set(id, new Map());
      for (const e of edges) {
        if (e.sourceId === e.targetId) continue;
        const a = adj.get(e.sourceId);
        const b = adj.get(e.targetId);
        Iif (a === undefined || b === undefined) continue;
        const existing = a.get(e.targetId) ?? 0;
        if (e.weight > existing) {
          a.set(e.targetId, e.weight);
          b.set(e.sourceId, e.weight);
        }
      }
      return adj;
    }

    /**
     * Breadth-first traversal capped at `maxDepth` hops from one or more seeds.
     *
     * Returns the set of node ids reachable within `maxDepth` hops (inclusive).
     * `maxDepth=1` returns only the seeds plus their direct neighbours;
     * `maxDepth=0` returns only the seeds themselves.
     *
     * @param adj - Adjacency map produced by {@link buildAdjacency}.
     * @param seeds - One or more starting node ids.
     * @param maxDepth - Non-negative hop limit.
     * @returns Set of reachable node ids.
     */
    /** Lex-compare helper for deterministic ordering. */
    function lexCompare(a: string, b: string): number {
      if (a < b) return -1;
      Eif (a > b) return 1;
      return 0;
    }

    /** Expand one BFS frontier into the next within an adjacency map. */
    function expandFrontier(
      adj: AdjacencyMap,
      frontier: readonly string[],
      visited: Set<string>
    ): string[] {
      const next: string[] = [];
      for (const node of frontier) {
        const neighbours = adj.get(node);
        Iif (neighbours === undefined) continue;
        const sortedNeighbours = [...neighbours.keys()].sort(lexCompare);
        for (const n of sortedNeighbours) {
          if (!visited.has(n)) {
            visited.add(n);
            next.push(n);
          }
        }
      }
      return next;
    }

    export function bfsLimited(adj: AdjacencyMap, seeds: readonly string[], maxDepth: number): Set<string> {
      const visited = new Set<string>();
      Iif (maxDepth < 0) return visited;
      let frontier: string[] = [];
      for (const s of seeds) {
        if (adj.has(s) && !visited.has(s)) {
          visited.add(s);
          frontier.push(s);
        }
      }
      for (let depth = 0; depth < maxDepth && frontier.length > 0; depth++) {
        frontier.sort(lexCompare);
        frontier = expandFrontier(adj, frontier, visited);
      }
      return visited;
    }

    /**
     * Weighted-degree centrality: sum of incident edge weights per node.
     *
     * @param nodeIds - Node universe (so isolates return 0 rather than be omitted).
     * @param edges - Weighted edges.
     * @returns Map from node id → summed incident weight.
     */
    export function weightedDegree(nodeIds: readonly string[], edges: readonly WeightedEdge[]): Map<string, number> {
      const out = new Map<string, number>();
      for (const id of nodeIds) out.set(id, 0);
      for (const e of edges) {
        Iif (e.sourceId === e.targetId) continue;
        Eif (out.has(e.sourceId)) out.set(e.sourceId, (out.get(e.sourceId) ?? 0) + e.weight);
        Eif (out.has(e.targetId)) out.set(e.targetId, (out.get(e.targetId) ?? 0) + e.weight);
      }
      return out;
    }

    /**
     * Brandes' betweenness centrality on a weighted undirected graph.
     *
     * Implements Dijkstra-based shortest-path counting from each source as
     * described in U. Brandes, *A Faster Algorithm for Betweenness Centrality*
     * (2001). Edge weights are interpreted as **similarity** — internally
     * converted to distance `1 / weight` so high-weight edges are "shorter"
     * and therefore preferred routes for brokers.
     *
     * Complexity: `O(V² · log V)` per source with the current array-backed
     * priority queue (each `popClosest` performs a full `Array.prototype.sort`
     * and `relaxShorter` uses `Array.prototype.includes`). A binary-heap
     * priority queue would lower this to the textbook `O(V · (V + E) · log V)`
     * bound but is not required for the small graphs this module is designed
     * for (V is capped at a few hundred nodes by the calling tool).
     *
     * The returned scores are normalised by `1 / ((V-1)(V-2))` for V≥3 (undirected
     * graph — each unordered pair is traversed twice during Brandes) so they
     * land in `[0, 1]`. For V<3, raw scores (all zero) are returned.
     *
     * @param nodeIds - Node universe (deterministic order is enforced internally).
     * @param edges - Weighted edges (similarity in `(0, 1]`).
     * @returns Map from node id → normalised betweenness in `[0, 1]`.
     */
    /** Brandes per-source Dijkstra state. */
    interface BrandesState {
      stack: string[];
      pred: Map<string, string[]>;
      sigma: Map<string, number>;
      dist: Map<string, number>;
    }

    function initBrandesState(nodes: readonly string[], source: string): BrandesState {
      const pred = new Map<string, string[]>();
      const sigma = new Map<string, number>();
      const dist = new Map<string, number>();
      for (const v of nodes) {
        pred.set(v, []);
        sigma.set(v, 0);
        dist.set(v, Number.POSITIVE_INFINITY);
      }
      sigma.set(source, 1);
      dist.set(source, 0);
      return { stack: [], pred, sigma, dist };
    }

    function popClosest(queue: string[], dist: Map<string, number>): string | undefined {
      queue.sort((a, b) => {
        const da = dist.get(a) ?? Number.POSITIVE_INFINITY;
        const db = dist.get(b) ?? Number.POSITIVE_INFINITY;
        if (da !== db) return da - db;
        return lexCompare(a, b);
      });
      return queue.shift();
    }

    function relaxShorter(state: BrandesState, queue: string[], v: string, w: string, alt: number): void {
      state.dist.set(w, alt);
      state.sigma.set(w, state.sigma.get(v) ?? 0);
      state.pred.set(w, [v]);
      Eif (!queue.includes(w)) queue.push(w);
    }

    function relaxEqual(state: BrandesState, v: string, w: string): void {
      state.sigma.set(w, (state.sigma.get(w) ?? 0) + (state.sigma.get(v) ?? 0));
      state.pred.get(w)?.push(v);
    }

    function relaxEdge(
      state: BrandesState,
      queue: string[],
      v: string,
      w: string,
      weight: number
    ): void {
      Iif (weight <= 0) return;
      const dv = state.dist.get(v) ?? Number.POSITIVE_INFINITY;
      const alt = dv + 1 / weight;
      const dw = state.dist.get(w) ?? Number.POSITIVE_INFINITY;
      if (alt < dw - 1e-12) relaxShorter(state, queue, v, w, alt);
      else if (Math.abs(alt - dw) < 1e-12) relaxEqual(state, v, w);
    }

    function runDijkstra(adj: AdjacencyMap, state: BrandesState, source: string): void {
      const queue: string[] = [source];
      while (queue.length > 0) {
        const v = popClosest(queue, state.dist);
        Iif (v === undefined) break;
        state.stack.push(v);
        const neighbours = adj.get(v);
        Iif (neighbours === undefined) continue;
        // Iterate neighbours in lex-sorted order so tie-breaking is fully
        // deterministic regardless of the underlying Map insertion order
        // (which depends on the input edge-list ordering).
        const sortedNeighbours = [...neighbours.keys()].sort(lexCompare);
        for (const w of sortedNeighbours) {
          const weight = neighbours.get(w);
          Iif (weight === undefined) continue;
          relaxEdge(state, queue, v, w, weight);
        }
      }
    }

    function propagateDelta(state: BrandesState, w: string, delta: Map<string, number>): void {
      const sw = state.sigma.get(w) ?? 0;
      const dw = delta.get(w) ?? 0;
      Iif (sw <= 0) return;
      for (const v of state.pred.get(w) ?? []) {
        const sv = state.sigma.get(v) ?? 0;
        delta.set(v, (delta.get(v) ?? 0) + (sv / sw) * (1 + dw));
      }
    }

    function accumulateBetweenness(
      state: BrandesState,
      source: string,
      nodes: readonly string[],
      cb: Map<string, number>
    ): void {
      const delta = new Map<string, number>();
      for (const v of nodes) delta.set(v, 0);
      while (state.stack.length > 0) {
        const w = state.stack.pop();
        Iif (w === undefined) break;
        propagateDelta(state, w, delta);
        if (w !== source) cb.set(w, (cb.get(w) ?? 0) + (delta.get(w) ?? 0));
      }
    }

    export function betweennessCentrality(
      nodeIds: readonly string[],
      edges: readonly WeightedEdge[]
    ): Map<string, number> {
      const sortedNodes = [...nodeIds].sort(lexCompare);
      const adj = buildAdjacency(sortedNodes, edges);
      const cb = new Map<string, number>();
      for (const v of sortedNodes) cb.set(v, 0);

      for (const s of sortedNodes) {
        const state = initBrandesState(sortedNodes, s);
        runDijkstra(adj, state, s);
        accumulateBetweenness(state, s, sortedNodes, cb);
      }

      const n = sortedNodes.length;
      if (n >= 3) {
        // Undirected graph: each unordered pair is traversed twice by Brandes
        // (once from each endpoint as source), so the normalisation factor is
        // 1 / ((n-1)(n-2)) rather than the directed 2 / ((n-1)(n-2)).
        const norm = 1 / ((n - 1) * (n - 2));
        for (const [k, v] of cb) cb.set(k, Math.round(v * norm * 10000) / 10000);
      }
      return cb;
    }

    /**
     * Deterministic asynchronous label propagation for community detection.
     *
     * Each node is initialised with its own label (its id). On every iteration
     * each node — visited in sorted id order — adopts the label that maximises
     * the **sum of edge weights** to neighbours sharing that label, with ties
     * broken by lexicographic label order. Labels are updated **in place** so
     * downstream nodes in the same sweep already see their predecessors'
     * decisions. This asynchronous variant avoids the oscillation that pure
     * synchronous label propagation exhibits on symmetric / bipartite graphs.
     *
     * As an additional safety bound the algorithm fingerprints the full label
     * vector after each sweep and stops if either:
     * - no label changed during the sweep (true convergence), or
     * - the fingerprint matches the previous-previous sweep (2-cycle).
     *
     * Sorted-order traversal plus deterministic tie-breaking guarantees
     * reproducible clusters across runs.
     *
     * @param nodeIds - Node universe.
     * @param edges - Weighted edges.
     * @param maxIterations - Safety bound (default 30, typically converges in <10).
     * @returns Map from node id → community label.
     */
    function runLabelIteration(
      sorted: readonly string[],
      adj: AdjacencyMap,
      labels: Map<string, string>
    ): boolean {
      let changed = false;
      // Asynchronous: update labels in place so each node in `sorted` sees the
      // most recent labels assigned earlier in the same sweep.
      for (const node of sorted) {
        const neighbours = adj.get(node);
        if (neighbours === undefined || neighbours.size === 0) continue;
        const score = aggregateNeighbourLabels(neighbours, labels);
        const bestLabel = pickBestLabel(score);
        if (bestLabel !== undefined && bestLabel !== labels.get(node)) {
          labels.set(node, bestLabel);
          changed = true;
        }
      }
      return changed;
    }

    /** Build a deterministic fingerprint of the current label vector. */
    function fingerprintLabels(sorted: readonly string[], labels: ReadonlyMap<string, string>): string {
      const parts: string[] = [];
      for (const id of sorted) parts.push(`${id}=${labels.get(id) ?? ''}`);
      return parts.join('|');
    }

    export function labelPropagation(
      nodeIds: readonly string[],
      edges: readonly WeightedEdge[],
      maxIterations = 30
    ): Map<string, string> {
      const sorted = [...nodeIds].sort(lexCompare);
      const adj = buildAdjacency(sorted, edges);
      const labels = new Map<string, string>();
      for (const id of sorted) labels.set(id, id);
      // Track the previous two fingerprints to detect 2-cycles (label vector
      // alternating between two states without converging).
      let prevPrint = '';
      let prevPrevPrint = '';
      for (let iter = 0; iter < maxIterations; iter++) {
        if (!runLabelIteration(sorted, adj, labels)) break;
        const print = fingerprintLabels(sorted, labels);
        Iif (print === prevPrevPrint) break;
        prevPrevPrint = prevPrint;
        prevPrint = print;
      }
      return labels;
    }

    /** Pick the label with the highest aggregated weight; ties broken lex-smallest. */
    function pickBestLabel(score: Map<string, number>): string | undefined {
      Iif (score.size === 0) return undefined;
      const sortedScores = [...score.entries()].sort((a, b) => lexCompare(a[0], b[0]));
      let bestLabel: string | undefined;
      let bestScore = -Infinity;
      for (const [lab, s] of sortedScores) {
        if (s > bestScore + 1e-12) {
          bestScore = s;
          bestLabel = lab;
        }
      }
      return bestLabel;
    }

    /** Aggregate weighted neighbour labels for a single node during label propagation. */
    function aggregateNeighbourLabels(
      neighbours: Map<string, number>,
      labels: Map<string, string>
    ): Map<string, number> {
      const score = new Map<string, number>();
      for (const [n, w] of neighbours) {
        const lab = labels.get(n);
        Iif (lab === undefined) continue;
        score.set(lab, (score.get(lab) ?? 0) + w);
      }
      return score;
    }

    /**
     * Newman's modularity Q for a weighted partition.
     *
     * `Q = (1 / 2m) Σ_{ij} [A_ij - k_i k_j / 2m] δ(c_i, c_j)`
     *
     * where `A_ij` is edge weight, `k_i` weighted degree, and `δ` the Kronecker
     * indicator for same-community. Q ∈ `[-0.5, 1]`; values >0.3 indicate
     * meaningful community structure.
     *
     * @param nodeIds - Node universe.
     * @param edges - Weighted edges.
     * @param labels - Community label per node (from {@link labelPropagation}).
     * @returns Modularity Q rounded to 4 decimal places (`0` when the graph is empty).
     */
    export function modularity(
      nodeIds: readonly string[],
      edges: readonly WeightedEdge[],
      labels: Map<string, string>
    ): number {
      let m2 = 0;
      for (const e of edges) m2 += 2 * e.weight;
      if (m2 === 0) return 0;
      const deg = weightedDegree(nodeIds, edges);
      let q = 0;
      // Edge contributions (A_ij).
      for (const e of edges) {
        if (labels.get(e.sourceId) === labels.get(e.targetId)) {
          q += 2 * e.weight; // undirected pair counted both directions
        }
      }
      // Expected-degree subtraction over all same-community pairs (including self).
      // Iterate in sorted order for deterministic floating-point accumulation.
      const sortedNodeIds = [...nodeIds].sort();
      for (const i of sortedNodeIds) {
        const li = labels.get(i);
        const ki = deg.get(i) ?? 0;
        for (const j of sortedNodeIds) {
          if (labels.get(j) !== li) continue;
          const kj = deg.get(j) ?? 0;
          q -= (ki * kj) / m2;
        }
      }
      return Math.round((q / m2) * 10000) / 10000;
    }