Self-similarity of edge weights and community detection in weighted networks

In this paper, we present the concept of self-similarity of edge weights, and propose a new definition of weighted communities, that groups of nodes in which the edge weights distribute uniformly but between which they distribute randomly, based on the concept. This definition of weighted communities is different form the conventional one that groups of nodes in which the edge weights are large while between which they are small, and can be used to reveal the steady connections between nodes or some similarity between nodes' functions. In order to detect such communities, we propose a corresponding weighted modularity QSW and a modified spectral optimization algorithm. We apply our method to several compute-generated networks and real networks, the experiment results clearly show the functions of our method. Furthermore, by changing λ which we use for evaluating the equivalence of edge weights, we can discover a special hierarchical organization describing the various steady connections between nodes in groups with our method. ©, 2015, Binary Information Press