Correlation of Node Importance Measures: An Empirical Study through Graph Robustness

Mirza Basim Baig, Leman Akoglu

Abstract: Graph robustness is a measure of resilience to failures and targeted attacks. A large body of research on robustness focuses on how to attack a given network by deleting a few nodes so as to maximally disrupt its connectedness. As a result, literature contains a myriad of attack strategies that rank nodes by their relative importance for this task. How different are these strategies? Do they pick similar sets of target nodes, or do they differ significantly in their choices? In this paper, we perform the first large scale empirical correlation analysis of attack strategies, i.e., the node importance measures that they employ, for graph robustness. We approach this task in three ways; by analyzing similarities based on (i) their overall ranking of the nodes, (ii) the characteristics of top nodes that they pick, and (iii) the dynamics of disruption that they cause on the network. Our study of 15 different (randomized, local, distance-based, and spectral) strategies on 68 real-world networks reveals surprisingly high correlations among node-attack strategies, consistent across all three types of analysis, and identifies groups of comparable strategies. These findings suggest that some computationally complex strategies can be closely approximated by simpler ones, and a few strategies can be used as a close proxy of the consensus among all of them.