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Efficiency of complex networks under failures and attacks: A percolation approach

Author

Listed:
  • Zhou, Yaoming
  • Wang, Junwei

Abstract

Network efficiency, defined as the average of the reciprocal of the shortest path lengths between each node pair in a network, indicates how efficiently the network propagates information. The change of efficiency caused by failures or attacks can be used to assess the robustness or resilience of networks. However, due to the uncertainties of failures or attacks, the lengths of the shortest paths and in turn efficiency in a disrupted network cannot be easily calculated. The normal practice in the literature is to estimate the efficiency in different scenarios by simulation. In this paper, we propose an analytical way to assess the efficiency of complex networks under failures and attacks using percolation theory. We find that the efficiency of an affected network is exactly the product of global connectivity and local connectivity, where global connectivity refers to the size of the giant component, and local connectivity represents the average number of neighbors with different distances. This approach not only provides a more efficient and systematic way to analyze efficiency, but also reveals the relation between efficiency and connectivity. We discuss the application of our approach to scale-free networks and random graphs.

Suggested Citation

  • Zhou, Yaoming & Wang, Junwei, 2018. "Efficiency of complex networks under failures and attacks: A percolation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 658-664.
  • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:658-664
    DOI: 10.1016/j.physa.2018.08.093
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