Identifying Local Clustering Structures of Evolving Social Networks Using Graph Spectra (Short Paper)

  • Bo Jiao
  • Yiping BaoEmail author
  • Jin Wang
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 268)


The clustering coefficient has been widely used for identifying the local structure of networks. In this paper, the weighted spectral distribution with 3-cycle (WSD3) that is similar (but not equal) to the clustering coefficient is studied on evolving social networks. It is demonstrated that the ratio of the WSD3 to the network size (i.e., the node number) provides a more sensitive discrimination for the size-independent local structure of social networks in contrast to the clustering coefficient. Moreover, the difference of the WSD3’s performances on social networks and communication networks is investigated, and it is found that the difference is induced by the different symmetrical features of the normalized Laplacian spectral densities on these networks.


Social networks Clustering coefficient Weighted spectral distribution Normalized Laplacian spectrum 



This research has been supported by the Open Fund Project of National Engineering Laboratory for Big Data Application on Improving Government Governance Capabilities.


  1. 1.
    Paluck, E.L., Shepherd, H., Aronow, P.M.: Changing climates of conflict: a social network experiment in 56 schools. Proc. Natl. Acad. Sci. 113(3), 566–571 (2016)CrossRefGoogle Scholar
  2. 2.
    Fay, D., Haddadi, H., Thomason, A., et al.: Weighted spectral distribution for internet topology analysis: theory and applications. IEEE/ACM Trans. Netw. 18(1), 164–176 (2010)CrossRefGoogle Scholar
  3. 3.
    Jiao, B., Shi, J., Wu, X., et al.: Correlation between weighted spectral distribution and average path length in evolving networks. Chaos Interdisc. J. Nonlinear Sci. 26(2), 023110 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Xie, P., Zhang, Z., Comellas, F.: The normalized Laplacian spectrum of subdivisions of a graph. Appl. Math. Comput. 286, 250–256 (2016)MathSciNetGoogle Scholar
  5. 5.
    Chen, M., Yu, B., Xu, P., et al.: A new deterministic complex network model with hierarchical structure. Phys. A Stat. Mech. Appl. 385(2), 707–717 (2007)CrossRefGoogle Scholar
  6. 6.
    Leskovec, J., Backstrom, L., Kumar, R., et al.: Microscopic evolution of social networks. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 462–470. ACM (2008)Google Scholar
  7. 7.
    Stanford Large Network Dataset Collection. Accessed 19 July 2018
  8. 8.
    Zhou, S., Mondragón, R.J.: Accurately modeling the Internet topology. Phys. Rev. E 70(6), 066108 (2004)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.CETC Big Data Research Institute Co., Ltd.GuiyangChina
  2. 2.School of Mathematics and Big DataFoshan UniversityFoshanChina
  3. 3.Guizhou Wingscloud Co., Ltd.GuiyangChina

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