fullseye

graph_rich_club_curve — GRAPH core op

• データ種: matrix → table
• 呼び出し: import fullseye as fs; fs.ledger.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0) (実装を直接呼ぶなら import graphinv; graphinv.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0)、台帳から引くなら opsgraph.get("graph_rich_club_curve"))

使い方

Rich-club coefficient φ(k) for every k, against the degree-preserving null.

φ(k) is the directed density of the subgraph spanned by the nodes whose degree exceeds k: edges among them / (r (r − 1)), r = their number (Colizza et al. 2006; the same formula as :func:conngraph.graph_rich_club, here for all k at once). mode is the degree used to rank nodes: "total" (in + out), "in" or "out" (Yadav & Singh 2026 rank by in- and out-degree separately). A rising φ(k) alone means little — high-degree nodes are dense in any graph — so φ is divided by its mean over n_null rewirings that keep every node’s in- and out-degree exactly (Maslov & Sneppen 2002; every sample is checked, fail-closed). ratio > 1 is the rich-club regime; Towlson et al. 2013 call it significant where ratio > 1 + sd.

Returns a dict: k (all integers 0 .. max degree − 1), count (nodes with degree

k), phi, null_mean, null_sd, ratio (nan where the null mean is 0), z (nan where the null sd is 0 – e.g. a complete graph, where no swap changes phi), regime (bool: ratio > 1 + null sd of the ratio), n_null, mode.

Identities: phi[k] == conngraph.graph_rich_club(adj, k) for every k with mode="total"; a complete graph has phi == 1 and ratio == 1 everywhere (no swap can change it); a rewired sample of the graph itself has ratio ≈ 1.

Raises ValueError: as :func:graph_degree_preserving_null (non-square, negative, … ; n_null < 2; swaps_per_edge < 1; fewer than 2 edges); mode not in / out / total.

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• poc_worm_core_persists — py -3.11 examples/poc_worm_core_persists.py

型が繋がる次の op(table を入力に取れる)

graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length

同カテゴリ(core)

graph_kcore

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Provenance: graphinv.py — GRAPH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.

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