Mixing patterns and communities on bipartite graphs on web-based social interactions

We use bipartite graph representation of interactions between users of Web databases, such as data about art subjects (books, movies, music records), where users interact via posting comments related to a specific subject. We study patterns of clustering which emerge through the common interests of users. We find robust scale-invariant features in several statistical measures, demonstrated with the data about movies, both in the bipartite and monopartite projections. We present evidence of disassortative mixing on the bipartite graphs which applies both for users and movies. With the spectral analysis of suitably projected weighted networks we find variety of communities, which are based on the properties of the subjects of common interests and of the user habits.