Revisiting Power-law Distributions in Spectra of Real World Networks

By studying a large number of real world graphs, we find empirical evidence that most real world graphs have a statistically significant power-law distribution with a cutoff in the singular values of the adjacency matrix and eigenvalues of the Laplacian matrix in addition to the commonly conjectured power-law in the degrees. Among these results, power-laws in the singular values appear more consistently than in the degree distribution. The...