core op• 数据种类:matrix → table
• 调用: import fullseye as fs; fs.ledger.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0)(要直接调用实现,import graphinv; graphinv.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0);从台账取用则 opsgraph.get("graph_rich_club_curve"))
> 该算子的说明尚无译文,以下照原文给出。
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 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 graph_degree_preserving_null (non-square, negative, ... ; n_null < 2; swaps_per_edge < 1; fewer than 2 edges); mode not in / out / total.
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者、年份)与用途见上面的族使用指南。
• poc_worm_core_persists — py -3.11 examples/poc_worm_core_persists.py
table 作为输入)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
core)*Provenance: graphinv.py — GRAPH 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.