Percolation on random networks with arbitrary k-core structure

Abstract

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.

9 pages, 5 figures

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• Predicting the diversity of early epidemic spread on networks
• Random Graphs with Prescribed $K$-Core Sequences: A New Null Model for Network Analysis
• Statistical analysis of edges and bredges in configuration model networks
• Coexistence of phases and the observability of random graphs
• Homophily Within and Across Groups
• Emergence of strongly connected giant components in continuum disk-spin percolation
• Improving the accuracy of the k-shell method by removing redundant links-from a perspective of spreading dynamics