Transitivity based community analysis and detection

This paper extends our previous effort in employing transitivity attributes of graphs for social network analysis. Specifically, here we focus on the problem of network community detection. We propose spectral analysis of the transitivity gradient matrix and compare our framework to the modularity based community detection that attracted many network researchers´ attention recently. Previously, we showed that the transitivity attributes of social networks can be analyzed within the resolution of individual links, helping analysts in bridging concepts from the micro- and macro- levels of social network analysis. In this paper, we show that for the problem of network community detection, a key advantage of using transitivity is that it quantifies the degree of community structure independent of the number and sizes of clusters or communities within the network. We employ a Gaussian mixture model in the spectral domain of the proposed transitivity gradient matrix for modeling communities. Performance of the proposed method is compared to the state-of-the-art modularity based community detection over randomly generated networks with social network characteristics such as scale-free degree distributions and high clustering coefficients.