Distance-generalized Core Decomposition
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The k-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least k other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of k-core, which we refer to as the (k,h)-core, i.e., the maximal subgraph in which every vertex has at least k other vertices at distance ≤ h within that subgraph. We study the properties of the (k,h)-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as h-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm.
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