Interplay between Social Influence and Network Centrality: A Comparative Study on Shapley Centrality and Single-Node-Influence Centrality

We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node’s significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function — formulated based on a fundamental cooperative-game-theoretical concept — to measure the significance of nodes. We present a comprehensive comparative study of these two centrality measures. Mathematically, we present axiomatic characterizations, which precisely capture the essence of these two centrality measures and their fundamental differences. Algorithmically, we provide scalable algorithms for approximating them for a large family of social-influence instances. Empirically, we demonstrate their similarity and differences in a number of real-world social networks, as well as the efficiency of our scalable algorithms. Our results shed light on their applicability: SNI centrality is suitable for assessing individual influence in isolation while Shapley centrality assesses individuals’ performance in group influence settings.