The evaluation function of weight similarity and its application in community detection in weighted networks

Abstract

An evaluation function of weight similarity in weighted network is proposed,and a spectral algorithm for detecting community structure based on the function is presented. The results show that the algorithm can divide the weighted network into several groups within each of them the edges weights distribute uniformly but at random between them. The algorithm is analyzed by constructing random weighted networks with known community structure. Compared with WEO and WGN,the algorithm has high accuracy when the threshold coefficient takes small values. For a network with n nodes and c communities,the computation complexity of the algorithm is O(cn2/2). By setting different threshold coefficients,a special hierarchical organization which describes the various steady connections between nodes in groups can be discovered by the algorithm. It is different from the conventional concept of community detection in weighted networks which divides the weighted network into several groups in which the edges weights are relatively larger than those in-between them,such that it extracts the information about the structure of weighted networks from another perspective.