A stable betweenness centrality measure in networks

This paper presents a formal definition of stability for node centrality measures in networks and shows that the well-known betweenness centrality is not stable with respect to that metric. An alternative definition that preserves the same centrality notion while satisfying this stability criterion is then introduced. The practical implications of stability are explored by studying the behavior of the traditional as well as the alternative stable betweenness centrality in both, synthetic random networks, and the network of interactions between sectors of the United States economy.