How Typical are Real Networks A Statistical Physics Study Senior Honors Thesis Department of Physics and Astronomy Northwestern University

Many dynamical processes on networks are bounded by the extreme eigenvalues of connectivity matrices. Based on these eigenvalues, we investigate how typical real networks are as compared to associated ensembles of random networks. Recent theory indicates that the eigenvalue distributions of random network ensembles are well represented by their means. Thus, if the real eigenvalues of a network are close to ensemble means, the real network is typical within the ensemble. Some of the networks studied here are deemed typical, but many appear to contain additional structure which is not captured by the simplest ensembles. To investigate this, effects of communities and low degree nodes are also explored.