Opinion maximization in social networks via link recommendation

Abstract

We study a variation of the Friedkin-Johnsen model for opinion dynamics in a leader-follower social network with n nodes and m edges, where the node set is partitioned into three subsets: set of leader nodes with opinion 1, set of leaders with opinion 0, and set of follower nodes. We give an explicit expression for the steady-state opinion vector in terms of some related matrices and the initial opinion vector, and interpret the equilibrium opinion vector as the weighted average of the initial opinions for all nodes with the weights being the escape probabilities of a defining random walk. We then pose an opinion maximization problem of recommending k new edges between 1-leader and follower nodes so that the equilibrium overall opinion is maximized. We show that the objective function is monotone and submodular, and propose a simple greedy algorithm with an approximation factor $(1-\frac{1}{e})$ that approximately solves the problem in cubic running time. To speed up the computation, we also provide a fast algorithm with an approximation ratio $(1-\frac{1}{e}-ϵ)$ and computation complexity $\tilde{O}\left(mk{ϵ}^{-2}\right)$ for any $ϵ>0$, where the $\tilde{O}(\cdot )$ notation suppresses the $\mathrm{poly}(\log n)$ factors. Extensive experiments on both real social networks with real opinions and datasets with synthetic opinions demonstrate that our algorithms are effective, efficient, and scale well to large social networks.