An Empirical Study of Robustness of Network Centrality Scores in Various Networks and Conditions

Network centrality score is an important measure to assess the importance and the major roles that each node plays in a network. In addition, the centrality score is also vitally important in assessing the overall structure and connectivity of a network. In a narrow sense, nearly all network mining algorithms, such as social network community detection, link predictions etc., involve certain types of centrality scores to some extent. Despite of its importance, very few researches have empirically analyzed the robustness of these measures in different network environments. Our existing works know very little about how network centrality score behaves at macro- (i.e. network) and micro- (i.e. individual node) levels. At the network level, what are the inherent connections between network topology structures and centrality scores? Will a sparse network be more (or less) robust in its centrality scores if any change is introduced to the network? At individual node levels, what types of nodes (high or low node degree) are more sensitive in their centrality scores, when changes are imposed to the network?And which centrality score is more reliable in revealing the genuine network structures? In this paper, we empirically analyze the robustness of three types of centrality scores: Betweenness centrality score, Closeness centrality score, and Eigen-vector centrality score for various types of networks. We systematically introduce biased and unbiased changes to the networks, by adding and removing different percentages of edges and nodes, through which we can compare and analyze the robustness and sensitivity of each centrality score measurement. Our empirical studies draw important findings to help understand the behaviors of centrality scores in different social networks.