An evolving network model with community structure
  Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analyzed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties. 
Chunguang Li, Philip K. Maini