Triangle k Core

Triangle k Core

Definition Triangle Core

The triangle k-core of a simple undirected graph $G=(V,E)$ is the inclusion maximal subgraph $C_{k}(G)\subset G$ where each edge $e\in E(C_{k}(G))$ is part of at least $k$ triangles in $C_{k}(G)$.

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Definition Triangle Core Number

The triangle core number of an edge $e\in E(G)$ is the maximal k such that $e\in C_{k}(G)$

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