A Dynamic Model for On-Line Social Networks

We present a deterministic model for on-line social networks based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model, at each time-step and for every existing node x, a new node appears which joins to the closed neighbour set of x. The ILT model provably satisfies a number of both local and global properties that were observed in real-world on-line social and other complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studies of social networks demonstrate poor expansion properties as a consequence of the existence of communities with low number of inter-community links. A spectral gap for both the adjacency and normalized Laplacian matrices is proved for graphs arising from the ILT model, thereby simulating such bad expansion properties.