Ensemble Averageability in Network Spectra

Dong-Hee Kim, Adilson E. Motter
2007 Physical Review Letters  
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
more » ... increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.
doi:10.1103/physrevlett.98.248701 pmid:17677999 fatcat:2cv6ty6gmvd3te6wx2a2uawcce