Bond and site color-avoiding percolation in scale-free networks

Andrea Kadović, Sebastian M. Krause, Guido Caldarelli, and Vinko Zlatic
Phys. Rev. E 98, 062308 – Published 10 December 2018

Abstract

Recently, the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one vulnerability (color), a robust color-avoiding connectivity is possible. However, many infrastructure networks show the problem of vulnerable classes of edges instead of vertices. Here we formulate color-avoiding percolation for colored edges as well. Additionally, we allow for random failures of vertices or edges. The interplay of random failures and possible collective failures implies a rich phenomenology. An interesting form of critical behavior is found for networks with a power-law degree distribution independent of the number of colors, but still dependent on the existence of the colors and therefore different from standard percolation. Our percolation framework fills a gap between different multilayer network percolation scenarios.

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  • Received 27 July 2018

DOI:https://doi.org/10.1103/PhysRevE.98.062308

©2018 American Physical Society

Physics Subject Headings (PhySH)

Networks

Authors & Affiliations

Andrea Kadović1, Sebastian M. Krause2, Guido Caldarelli3,4,5,6, and Vinko Zlatic1,4

  • 1Division of Theoretical Physics, Rudjer Bošković Institute, Zagreb, Croatia
  • 2Faculty of Physics, University of Duisburg–Essen, Duisburg, Germany
  • 3IMT School for Advanced Studies Lucca, Piazza San Francesco 19, 55100 Lucca, Italy
  • 4CRN Institute for Complex Systems, via dei Taurini 19, 00185 Rome, Italy
  • 5London Institute for Mathematical Sciences, 35a South Street Mayfair, W1K 2XF London, United Kingdom
  • 6Linkalab, Complex Systems Computational Laboratory, Viale Elmas, 142 09122 Cagliari, Italy

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Issue

Vol. 98, Iss. 6 — December 2018

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