Global decomposition of networks into multiple cores formed by local hubs

Abstract

Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking inside, using the concept of locally defined nodal hub centrality and edge-pruning techniques built upon it. We demonstrate that the hub-centrality-based edge pruning reveals a series of breaking points in network decomposition, which effectively separates a network into its backbone and shell structures. Our local-edge decomposition method iteratively identifies and removes locally least connected nodes, and uncovers an onion-like hierarchical structure as a result. Compared with the conventional $k$-core decomposition method, our method based on relative information residing in local structures exhibits a clear advantage in terms of discovering locally crucial substructures. As an application of the method, we present a scheme to detect multiple core-periphery structures and the decomposition of coarse-grained supernode networks, by combining the method with the network community detection.

arXiv comment12 pages, 11 figures, 1 table

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