We present a model of evolution of large social networks. Our model is based on the local nature of communication: a node's communication energy is spend mostly within it's small social area. We test our model on the Blog network hosted by LiveJournal. Our testing with different definitions of local areas shows that the best approximation to the observed statistics occurs when the area is defined as the union of clusters containing the node, and when nodes communicate with other nodes within their area using a preferential attachment strategy. We define clusters as locally maximally dense sets of vertices; our definition allows for clusters to overlap.
Mark K. Goldberg, Malik Magdon-Ismail, Stephen Kel