摘要：In this paper, we present a Weighted Filtration Coefficient (WFC) ψ and a corresponding filtration method to detect the communities in weighted networks. In our method, a weighted network can be divided into groups by recursive filtration operations, and the dividing resuhs are evaluated by the ψ. We prove that optimization on local ψ enables us to obtain maximal global weighted modularity Q~w , which corresponds to the correct communities. For a weighted network with m edges and c communities, the weighted communities can be detected in time O((c + 1)m) , which is in linear scale time with the number of edges. Furthermore, the local weighted communities can be detected in an increasing order according to the edge weights between them. This division can reveal different levels of close connections between the nodes.
