Disentangling giant component and finite cluster contributions in sparse random matrix spectra

Phys Rev E. 2016 Apr;93:042110. doi: 10.1103/PhysRevE.93.042110. Epub 2016 Apr 12.

Abstract

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.