core op• データ種: matrix → table
• 呼び出し: import fullseye as fs; fs.ledger.graph_kcore(adj, mode='total', weighted=False) (実装を直接呼ぶなら import graphinv; graphinv.graph_kcore(adj, mode='total', weighted=False)、台帳から引くなら opsgraph.get("graph_kcore"))
配線行列の k-core(重み付きなら s-core)分解: 各節点の核の指数。入次数・出次数・総次数・無向のどれで剥くかを選ぶ。定理が門(完全グラフは n−1、木は 1、閉路は 2)。最深殻の節点、殻ごとの個数を返す。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
A k-core is the maximal subgraph in which every node has degree at least k (Seidman 1983); a node's core index is the largest k of a core it belongs to. mode picks the degree: "in" (inputs a node receives), "out", "total" (in + out; a reciprocal pair counts twice, as in conngraph.graph_rich_club) or "undirected" (an edge in either direction counts once — this is what networkx.core_number computes on the symmetrised graph). With weighted=True the degree is the strength (sum of weights, e.g. synapse counts) and the result is the s-core of Eidsaa & Almaas 2013: the index is the running maximum of the minimum strength during peeling, so it is a real number with the units of the weights. Self-loops are dropped.
Returns a dict: core (n,) — the index per node (int for k-core, float for s-core); kmax — the innermost index; inner (n,) bool — nodes of the innermost core; n_inner; levels — the distinct indices in increasing order and counts — how many nodes have each (sum(counts) == n); mode; weighted.
Identities (the tests): a complete graph on n nodes has every index n−1; a tree 1; a cycle 2; undirected agrees with networkx.core_number on random graphs; the s-core of a 0/1 matrix equals the k-core; multiplying every weight by c multiplies every s-core index by c; the innermost core is never empty and every one of its nodes has at least kmax (weighted: strength) inside the core.
Raises ValueError: as graph_degree_summary (non-square, negative, non-finite, string / bool / complex / masked input); mode not one of in / out / total / undirected.
• 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.