Robustness of Centrality Measures: The Stochastic Kronecker Graph Simulation Approach

Abstract

This paper tests the robustness of four centrality measures – degree, betweenness, closeness, and eignvector centrality – using graphs simulating real world networks by Stochastic Kronecker Graphs approach. Existing studies have used Erdos-Renyi (1959) random graphs which are poor match for real world networks. Stochastic Kronecker Graphs have been found to display real world network properties. Results suggest revision of some conclusions arrived at using random graphs. Mistakes in recording nodes affect accuracy of centrality measures more than mistakes in recording connections (edges). This supports conventional wisdom, and seeks revision of Borgatti et al. (2006). Supporting some existing studies, betweenness was found to be most robust of these four centrality measures, and closeness the least robust. This paper also demonstrates how confidence intervals around centrality measures can be created using simulation to help arrive at robust analysis.