Modeling interest-based social networks: Superimposing Erdős-Rényi graphs over random intersection graphs

There is a recent rise of interest-based social networks (e.g., Pinterest and Goodreads), which connect users by relations based on shared interests. In these networks, links between users manifest from selecting common interests from a pool of available interests. For example, two users may establish a link on Pinterest because of both liking dog photos, or on Goodreads due to reading the same novel. In this paper, we introduce a random graph model to represent an interest-based social network, in consideration of users’ shared interests as well as their friend relations. More specifically, the graph model is the result of superimposing an Erdős–Rényi graph (representing friendships) over a uniform random d-intersection graph (representing common interests). We present critical conditions of the model parameters so that the network is connected. Our connectivity results are useful to understand interest-based social networks and particularly beneficial for publish-subscribe services in these networks. The formally-proved results are also confirmed via experiments.