Network extreme eigenvalue : from mutimodal to scale-free networks
Chung, Ning Ning
Chew, Lock Yue
Lai, Choy Heng
Date of Issue2012
School of Physical and Mathematical Sciences
The extreme eigenvalues of adjacency matrices are important indicators on the influence of topological structures to the collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme eigenvalue have further authenticated its applicability to the study of network dynamics. However, the ensemble average of extreme eigenvalue has only been solved analytically up to the second order correction. Here, we determine the ensemble average of the extreme eigenvalue and characterize its deviation across the ensemble through the discrete form of random scale-free network. Remarkably, the analytical approximation derived from the discrete form shows significant improvement over previous results, which implies a more accurate prediction of the epidemic threshold. In addition, we show that bimodal networks, which are more robust against both random and targeted removal of nodes, are more vulnerable to the spreading of diseases.
Chaos: an interdisciplinary journal of nonlinear science
© 2012 American Institute of Physics. This paper was published in Chaos: An Interdisciplinary Journal of Nonlinear Science and is made available as an electronic reprint (preprint) with permission of American Institute of Physics. The paper can be found at the following official DOI: [http://dx.doi.org/10.1063/1.3697990]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.