A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Abstract

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> nodes problem and 2) λ -coverage problem. In the top- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> nodes problem, we are required to find a set of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> key nodes that would maximize the number of nodes being influenced in the network. The λ-coverage problem is concerned with finding a set of key nodes having minimal size that can influence a given percentage λ of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> nodes problem and the λ -coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient.