  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.
