{
 "_script": "scripts/compute-centrality.mjs",
 "_source": "data/association/*.json (PR 1; each root's top 25 partners by LLR, itself derived from Leeds Quranic Arabic Corpus v0.4 via scripts/compute-association-stats.mjs) and data/roots-summary.json (raw frequency).",
 "_graph": {
  "nodes": 1642,
  "edges": 5211,
  "edgeThresholdSharedVerses": 5,
  "note": "Edges are the union of every (root, partner) pair recorded in any root's data/association/ top-25-by-LLR partner list, not the full set of all pairs meeting the 5-shared-verse threshold corpus-wide (PR 1 reports 8,556 such pairs before the top-25-per-root cut). This graph is a subset by construction, since data/association/ was never designed to expose the full pair set and this script does not modify or extend it."
 },
 "_algorithms": {
  "degree": "Count of distinct neighbors (raw); normalized = raw / (N-1).",
  "weightedDegree": "Sum of incident edge weights (LLR); also called strength.",
  "betweenness": "Brandes' algorithm (2001), O(V*E), on the unweighted graph (every edge length 1; edge weight ignored for shortest-path computation).",
  "eigenvector": "Power iteration on the weighted adjacency matrix (edge weight = LLR): x_0 = uniform (every node = 1); x_{k+1} = A * x_k, L2-normalized; tolerance 1e-9, max 1000 iterations.",
  "spearmanCorrelation": "Tie-corrected: Pearson correlation of average ranks (standard Spearman's rho with ties)."
 },
 "_eigenvector": {
  "converged": true,
  "iterations": 178,
  "tolerance": 1e-9,
  "maxIterations": 1000
 },
 "_spearmanVsRawFrequency": {
  "degree": 0.8565,
  "weightedDegree": 0.8467,
  "betweenness": 0.7754,
  "eigenvector": 0.8402
 },
 "_computed": "2026-08-01"
}