Vulnerability of networks: Fractional percolation on random graphs

Shang, Yilun (2014) Vulnerability of networks: Fractional percolation on random graphs. Physical Review E, 89 (1). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.89.012813

Abstract

We present a theoretical framework for understanding nonbinary, nonindependent percolation on networks with general degree distributions. The model incorporates a partially functional (PF) state of nodes so that both intensity and extensity of error are characterized. Two connected nodes in a PF state cannot sustain the load and therefore break their link. We give exact solutions for the percolation threshold, the fraction of giant cluster, and the mean size of small clusters. The robustness-fragility transition point for scale-free networks with a degree distribution pk∝k−α is identified to be α=3. The analysis reveals that scale-free networks are vulnerable to targeted attack at hubs: a more complete picture of their Achilles' heel turns out to be not only the hubs themselves but also the edges linking them together.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Paul Burns
Date Deposited: 12 Dec 2018 16:00
Last Modified: 12 Dec 2018 16:00
URI: http://nrl.northumbria.ac.uk/id/eprint/37219

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