Estrada, Ernesto and Hatano, N. (2010) A vibrational approach to node centrality and vulnerability in complex networks. Physica A: Statistical Mechanics and its Applications, 389 (17). pp. 36483660. ISSN 03784371

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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.
Item type:  Article 

ID code:  28254 
Keywords:  Network vibrations, Centrality, Spectral theory, Kirchhoff index, Information centrality, Social networks, Mathematics, Physics, Statistics and Probability, Condensed Matter Physics 
Subjects:  Science > Mathematics Science > Physics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  14 Oct 2010 15:26 
Last modified:  27 Mar 2015 08:05 
URI:  http://strathprints.strath.ac.uk/id/eprint/28254 
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