IDEAS home Printed from
   My bibliography  Save this article

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


  • Zhou, Yaoming
  • Wang, Junwei


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

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:658-664. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.