A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks

TL;DR

This paper introduces a novel vibrational method to assess node vulnerability in complex networks by modeling nodes as balls and links as springs, linking physical vibrations to network centrality measures.

Contribution

It presents a new vulnerability measure based on node vibrations, establishing exact relations with existing centrality metrics and demonstrating improved resolution of node vulnerability.

Findings

Node displacement correlates with network vulnerability.

Exact relations are established between displacement, information centrality, and Kirchhoff index.

Vibrational measure offers better vulnerability resolution than traditional centrality.

Abstract

We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.