Identifying Local Clustering Structures of Evolving Social Networks Using Graph Spectra (Short Paper)
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.
KeywordsSocial 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.
- 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.Stanford Large Network Dataset Collection. http://snap.stanford.edu/data/. Accessed 19 July 2018