IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v378y2007i1p11-19.html
   My bibliography  Save this article

Percolation theory and fragmentation measures in social networks

Author

Listed:
  • Chen, Yiping
  • Paul, Gerald
  • Cohen, Reuven
  • Havlin, Shlomo
  • Borgatti, Stephen P.
  • Liljeros, Fredrik
  • Eugene Stanley, H.

Abstract

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, P∞, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erdős–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q of nodes above criticality, P∞≈(1-F)1/2. For fixed P∞ and close to criticality, we show that 1-F better reflects the actual fragmentation. For a given P∞, 1-F has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F and the percolation measure P∞ for a real national social network of workplaces linked by the households of the employees and find similar results.

Suggested Citation

  • Chen, Yiping & Paul, Gerald & Cohen, Reuven & Havlin, Shlomo & Borgatti, Stephen P. & Liljeros, Fredrik & Eugene Stanley, H., 2007. "Percolation theory and fragmentation measures in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(1), pages 11-19.
    • Handle: RePEc:eee:phsmap:v:378:y:2007:i:1:p:11-19
    DOI: 10.1016/j.physa.2006.11.074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106012611
    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
    File URL: https://libkey.io/10.1016/j.physa.2006.11.074?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Drago, Carlo & Ricciuti, Roberto, 2017. "Communities detection as a tool to assess a reform of the Italian interlocking directorship network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 91-104.
    2. Dong, Gaogao & Tian, Lixin & Du, Ruijin & Fu, Min & Stanley, H. Eugene, 2014. "Analysis of percolation behaviors of clustered networks with partial support–dependence relations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 370-378.
    3. Ding, Li & Guan, Zhi-Hong, 2008. "Modeling wireless sensor networks using random graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 3008-3016.
    4. Bu, Zhan & Xia, Zhengyou & Wang, Jiandong & Zhang, Chengcui, 2013. "A last updating evolution model for online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2240-2247.
    5. Zhukov, Dmitry & Khvatova, Tatiana & Lesko, Sergey & Zaltcman, Anastasia, 2018. "Managing social networks: Applying the percolation theory methodology to understand individuals' attitudes and moods," Technological Forecasting and Social Change, Elsevier, vol. 129(C), pages 297-307.

    Corrections

    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:378:y:2007:i:1:p:11-19. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.