Ensemble averageability in network spectra

Details Ensemble averageability in network spectra Ensemble averageability in network spectra

2007-05-09

arxiv.org/abs/0705.1175v2

Phys. Rev. Lett. 98, 248701 (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.98.248701

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.

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