Branching processes reveal influential nodes in social networks

Branching processes are discrete-time stochastic processes which have been largely employed to model and simulate information diffusion processes over large online social networks such as Twitter and Reddit. Here we show that a variant of the branching process model enables the prediction of the popularity of user-generated content and thus can serve as a method for ranking search results or suggestions displayed to users. The proposed branching-process variant is able to evaluate the importance of an agent in a social network and, thus we propose a novel centrality index, called the Stochastic Potential Gain (SPG). The SPG is the first centrality index which combines the knowledge of the network topology with a dynamic process taking place on it which we call a graph-driven branching process. SPG generalises a range of popular network centrality metrics such as Katz' and Subgraph. We formulate a Monte Carlo algorithm (called MCPG) to compute the SPG and prove that it is convergent and correct. Experiments on two real datasets drawn from Facebook and GitHub demonstrate that MCPG traverses only a small fraction of nodes to produce its result, thus making the Stochastic Potential Gain an appealing option to compute node centrality measure for Online social networks.