Mining Large Networks with Subgraph Counting

The problem of mining frequent patterns in networks has many applications, including analysis of complex networks, clustering of graphs, finding communities in social networks, and indexing of graphical and biological databases. Despite this wealth of applications, the current state of the art lacks algorithmic tools for counting the number of subgraphs contained in a large network. In this paper we develop data-stream algorithms that approximate the number of all subgraphs of three and four vertices in directed and undirected networks. We use the frequency of occurrence of all subgraphs to prove their significance in order to characterize different kinds of networks: we achieve very good precision in clustering networks with similar structure. The significance of our method is supported by the fact that such high precision cannot be achieved when performing clustering based on simpler topological properties, such as degree, assortativity, and eigenvector distributions. We have also tested our techniques using swap randomization.