title: Network extreme eigenvalue: from mutimodal to scale-free networks.
abstract: 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.
authors.affiliation: Temasek Laboratories, National University of Singapore, Singapore.
authors.forename: N N
authors.initials: NN
authors.lastname: Chung
authors.forename: L Y
authors.initials: LY
authors.lastname: Chew
authors.forename: C H
authors.initials: CH
authors.lastname: Lai
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*