Ensemble averageability in network spectra

Abstract

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.

4 pages, 4 figures

References in corpus (4)

• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic systems
• Dynamics on Complex Networks and Applications

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