Distribution-Free Models for Community Detection

Community detection for un-weighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. In this paper, a Distribution-Free Models (DFM) is proposed for networks in which nodes are partitioned into different communities. DFM is a general, interpretable and identifiable model for both un-weighted networks and weighted networks. The proposed model does not require prior knowledge on a specific distribution for elements of adjacency matrix but only the expected value. The distribution-free property of DFM even allows adjacency matrix to have negative elements. We develop an efficient spectral algorithm to fit DFM. By introducing a noise matrix, we build a theoretic framework on perturbation analysis to show that the proposed algorithm stably yields consistent community detection under DFM. Numerical experiments on both synthetic networks and two social networks from literature are used to illustrate the algorithm.