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Methods to find community based on edge centrality

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  • Sun, Peng Gang
  • Yang, Yang

Abstract

Divisive algorithms are of great importance for community detection in complex networks. One algorithm proposed by Girvan and Newman (GN) based on an edge centrality named betweenness, is a typical representative of this field. Here we studied three edge centralities based on network topology, walks and paths respectively to quantify the relevance of each edge in a network, and proposed a divisive algorithm based on the rationale of GN algorithm for finding communities that removes edges iteratively according to the edge centrality values in a certain order. In addition, we gave a comparison analysis of these measures with the edge betweenness and information centrality. We found the principal difference among these measures in the partition procedure is that the edge centrality based on walks first removes the edge connected with a leaf vertex, but the others first delete the edge as a bridge between communities. It indicates that the edge centrality based on walks is harder to uncover communities than other edge centralities. We also tested these measures for community detection. The results showed that the edge information centrality outperforms other measures, the edge centrality based on walks obtains the worst results, and the edge betweenness gains better performance than the edge centrality based on network topology. We also discussed our method’s efficiency and found that the edge centrality based on walks has a high time complexity and is not suitable for large networks.

Suggested Citation

  • Sun, Peng Gang & Yang, Yang, 2013. "Methods to find community based on edge centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1977-1988.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:1977-1988
    DOI: 10.1016/j.physa.2012.12.024
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

    1. Gao, Cai & Wei, Daijun & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2013. "A modified evidential methodology of identifying influential nodes in weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5490-5500.
    2. Li, Huajiao & An, Haizhong & Huang, Jiachen & Huang, Xuan & Mou, Songtao & Shi, Yanli, 2016. "The evolutionary stability of shareholders’ co-holding behavior for China’s listed energy companies based on associated maximal connected sub-graphs of derivative holding-based networks," Applied Energy, Elsevier, vol. 162(C), pages 1601-1607.
    3. Sun, Peng Gang, 2015. "Community detection by fuzzy clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 408-416.
    4. Du, Yuxian & Gao, Cai & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2014. "A new method of identifying influential nodes in complex networks based on TOPSIS," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 57-69.
    5. Li, Huajiao & An, Haizhong & Gao, Xiangyun & Huang, Jiachen & Xu, Qun, 2014. "On the topological properties of the cross-shareholding networks of listed companies in China: Taking shareholders’ cross-shareholding relationships into account," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 80-88.
    6. A. Tabrizi, Shayan & Shakery, Azadeh & Asadpour, Masoud & Abbasi, Maziar & Tavallaie, Mohammad Ali, 2013. "Personalized PageRank Clustering: A graph clustering algorithm based on random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5772-5785.
    7. Sun, Peng Gang & Sun, Xiya, 2017. "Complete graph model for community detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 88-97.

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