Resistance distance, information centrality, node vulnerability and vibrations in complex networks

Abstract

We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability. We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality. © 2010 Springer-Verlag London Limited.