Robustness of onionlike correlated networks against targeted attacks

Toshihiro Tanizawa, Shlomo Havlin, and H. Eugene Stanley
Phys. Rev. E 85, 046109 – Published 17 April 2012

Abstract

Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], using simulations, that scale-free networks with “onion structure” are very robust against targeted high degree attacks. The onion structure is a network where nodes with almost the same degree are connected. Motivated by this work, we propose and analyze, based on analytical considerations, an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks. The nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs,the degrees and populations of whose nodes are specified by the degree distribution. This network structure exhibits an extremely assortative degree-degree correlation and has a close relationship to the “onion structure.” After deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal, we apply the theory to the cases of random scale-free networks that are highly vulnerable against targeted high degree node removal. Our results show that this vulnerability can be significantly reduced by implementing this onionlike type of degree-degree correlation without much undermining the almost complete robustness against random node removal. We also investigate in detail the robustness enhancement due to assortative degree-degree correlation by introducing a joint degree-degree probability matrix that interpolates between an uncorrelated network structure and the onionlike structure proposed here by tuning a single control parameter. The optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined. Our analytical calculations are supported by numerical simulations.

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  • Received 20 December 2011

DOI:https://doi.org/10.1103/PhysRevE.85.046109

©2012 American Physical Society

Authors & Affiliations

Toshihiro Tanizawa1,*, Shlomo Havlin2, and H. Eugene Stanley3

  • 1Kochi National College of Technology, 200-1 Monobe-Otsu, Nankoku, Kochi 783-8508, Japan
  • 2Minerva Center and Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
  • 3Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA

  • *tanizawa@ee.kochi-ct.ac.jp

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Issue

Vol. 85, Iss. 4 — April 2012

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