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Title: Node importance for dynamical process on networks : a multiscale characterization
Authors: Zhang, J
Xu, X
Li, P
Zhang, K
Small, M
Issue Date: Mar-2011
Source: Chaos, Mar. 2011, v. 21, no. 1, 016107, p. 1-6
Abstract: Defining the importance of nodes in a complex network has been a fundamental problem in analyzing the structural organization of a network, as well as the dynamical processes on it. Traditionally, the measures of node importance usually depend either on the local neighborhood or global properties of a network. Many real-world networks, however, demonstrate finely detailed structure at various organization levels, such as hierarchy and modularity. In this paper, we propose a multiscale node-importance measure that can characterize the importance of the nodes at varying topological scale. This is achieved by introducing a kernel function whose bandwidth dictates the ranges of interaction, and meanwhile, by taking into account the interactions from all the paths a node is involved. We demonstrate that the scale here is closely related to the physical parameters of the dynamical processes on networks, and that our node-importance measure can characterize more precisely the node influence under different physical parameters of the dynamical process. We use epidemic spreading on networks as an example to show that our multiscale node-importance measure is more effective than other measures.
Keywords: Complex networks
Publisher: American Institute of Physics
Journal: Chaos 
ISSN: 1054-1500
EISSN: 1089-7682
DOI: 10.1063/1.3553644
Rights: © 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Zhang et al., Chaos: an interdisciplinary journal of nonlinear science 21, 016107 (2011) and may be found at
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