A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks

Details A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks A Vibrational Approach to Node Centrality and Vulnerability in Complex Networks

2009-12-22

arxiv.org/abs/0912.4307v1

Physica A 389 (2010) 3648-3660

Physics

Physics and Society

27 pages

Scientific paper

10.1016/j.physa.2010.03.030

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.

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