🤖 AI Summary
This paper addresses the challenge of effectively identifying and decomposing multi-scale core-periphery structures in complex networks. We propose a local-hub-centrality-driven edge-pruning network decomposition method that iteratively removes the least important nodes while adaptively pruning edges, thereby constructing an onion-like hierarchical architecture capable of detecting both intra-community multiple cores and supra-node-level cores. Our contributions are threefold: (1) we replace the global thresholding of classical k-core decomposition with a local hub centrality–guided decomposition paradigm; (2) we introduce a core-periphery scoring function enabling quantitative separation of structural roles; and (3) we unify core detection across both community-scale and supra-node-scale levels. Extensive experiments on diverse real-world networks demonstrate that our method significantly enhances the identification of local critical substructures, successfully disentangles hierarchically nested core-periphery organizations, and uncovers deep interdependencies between communities and supra-nodes.
📝 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 important 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. Furthermore, we introduce the core-periphery score to properly separate the core and periphery with our decomposition scheme. By extending the method combined with the network community structure, we successfully detect multiple core-periphery structures by decomposition inside each community. Moreover, the application of our decomposition to supernode networks defined from the communities reveals the intricate relation between the two representative mesoscale structures.