A Fast Algorithm for Ranking Users by their Influence in Online Social Platforms

Measuring the influence of users in social networks is key for numerous applications. A recently proposed influence metric, coined as $\psi$-score, allows to go beyond traditional centrality metrics, which only assess structural graph importance, by further incorporating the rich information provided by the posting and re-posting activity of users. The $\psi$-score is shown in fact to generalize PageRank for non-homogeneous node activity. Despite its significance, it scales poorly to large datasets; for a network of $N$ users, it requires to solve $N$ linear systems of equations of size $N$. To address this problem, this work introduces a novel scalable algorithm for the fast approximation of $\psi$-score, named \textit{Power}-$\psi$. The proposed algorithm is based on a novel equation indicating that it suffices to solve one system of equations of size $N$ to compute the $\psi$-score. Then, our algorithm exploits the fact that such a system can be recursively and distributedly approximated to any desired error. This permits the $\psi$-score, summarizing both structural and behavioral information for the nodes, to run as fast as PageRank. We validate the effectiveness of the proposed algorithm, which we release as an open source Python library, on several real-world datasets.