core op• Datenarten: matrix → table
• Aufruf: import fullseye as fs; fs.ledger.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0) (die Implementierung direkt: import graphinv; graphinv.graph_rich_club_curve(adj, mode='total', n_null=20, swaps_per_edge=5, seed=0); aus dem Register: opsgraph.get("graph_rich_club_curve"))
> Für diesen Operator gibt es noch keine Übersetzung. Es folgt der Originaltext unverändert.
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.
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• poc_worm_core_persists — py -3.11 examples/poc_worm_core_persists.py
table als Eingabe)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
core)*Provenance: graphinv.py — GRAPH Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.