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"))
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, 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.
• 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。
• poc_worm_core_persists — py -3.11 examples/poc_worm_core_persists.py
table を入力に取れる)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
core)*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.