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

We study network centrality based on dynamic influencepropagation models in social networks. To illustrate our in-tegrated mathematical-algorithmic approach for understand-ing the fundamental interplay between dynamic influenceprocesses and static network structures, we focus on twobasic centrality measures: (a) Single Node Influence (SNI)centrality, which measures each node’s significance by itsinfluence spread; and (b) Shapley Centrality, which usesthe Shapley value of the influence spread function — formu-lated based on a fundamental cooperative-game-theoreticalconcept — to measure the significance of nodes. We presenta comprehensive comparative study of these two centralitymeasures. Mathematically, we present axiomatic character-izations, which precisely capture the essence of these twocentrality measures and their fundamental differences. Al-gorithmically, we provide scalable algorithms for approxi-mating them for a large family of social-influence instances.Empirically, we demonstrate their similarity and differencesin a number of real-world social networks, as well as the effi-ciency of our scalable algorithms. Our results shed light ontheir applicability: SNI centrality is suitable for assessingindividual influence in isolation while Shapley centrality as-sesses individuals’ performance in group influence settings.