A vibrational approach to node centrality and vulnerability in complex networks

Ernesto Estrada and Naomichi Hatano

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 17, 3648-3660

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.

Keywords: Network vibrations; Centrality; Spectral theory; Kirchhoff index; Information centrality; Social networks (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:17:p:3648-3660

DOI: 10.1016/j.physa.2010.03.030

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