Interplay between Social Influence and Network Centrality: Shapley Values and Scalable Algorithms

A basic concept in network analysis is centrality, which measures the importance of nodes in a network. In this research, we address the following fundamental question: "Given a social network, what is the impact of the social influence models on network centrality?" Social influence is commonly formulated as a stochastic process, which defines how each group of nodes can collectively influence other nodes in an underlying graph. This process defines a natural cooperative game, in which each group's utility is its influence spread. Thus, fundamental game-theoretical concepts of this social-influence game can be instrumental in understanding network influence. We present a comprehensive analysis of the effectiveness of the game-theoretical approach to capture the impact of influence models on centrality. In this paper, we focus on the Shapley value of the above social-influence game. Algorithmically, we give a scalable algorithm for approximating the Shapley values of a large family of social-influence instances. Mathematically, we present an axiomatic characterization which captures the essence of using the Shapley value as the centrality measure to incorporate the impact of social-influence processes. We establish the soundness and completeness of our representation theorem by proving that the Shapley value of this social-influence game is the unique solution to a set of natural axioms for desirable centrality measures to characterize this interplay. The dual axiomatic-and-algorithmic characterization provides a comparative framework for evaluating different centrality formulations of influence models. Empirically, through a number of real-world social networks --- both small and large --- we demonstrate the important features of the Shapley centrality as well as the efficiency of our scalable algorithm.