k-Core Decomposition

k-Core Decomposition is a graph-theoretic method that partitions the vertices of a network into a nested sequence of subgraphs called k-cores. A k-core is the maximal subgraph in which every vertex has at least k neighbors within that subgraph. Introduced by Stephen B. Seidman in 1983, the method assigns each vertex a coreness number that captures its structural centrality relative to the local connectivity of the graph.