Global decomposition of networks into multiple cores formed by local hubs

TL;DR

This paper presents a novel network decomposition method based on local hub centrality and edge pruning, revealing multiscale core-periphery structures and hierarchical onion-like layers, outperforming traditional k-core approaches.

Contribution

The authors introduce a local hub-based edge pruning technique for multiscale network decomposition, uncovering hierarchical core-periphery structures and improving upon k-core methods.

Findings

Reveals multiscale core-periphery structures in networks.

Uncovers onion-like hierarchical network layers.

Effectively separates backbone and shell structures.

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.