Global decomposition of networks into multiple cores formed by local hubs
<|reference_start|>Global decomposition of networks into multiple cores formed by local hubs: 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.<|reference_end|>
@article{jeong2024global,
    title={Global decomposition of networks into multiple cores formed by local
  hubs},
    author={Wonhee Jeong, Unjong Yu, Sang Hoon Lee},
    journal={arXiv preprint arXiv:2407.00355},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00355},
    primaryClass={physics.soc-ph cond-mat.stat-mech cs.SI}
}