Fig. 8

Comparison of eigenvector components of the graph Laplacian in the Erdös–Rényi and Gaussian ensembles. Numerical evidence illustrating that the eigenvector components of the graph Laplacian for the symmetric Erdös–Rényi random graph ensemble are close to Gaussian distributed (to one standard deviation). Left: quantile–quantile plot for a Gaussian random matrix with $\mathcal{N}(0,1/50)$ entries. Right: quantile–quantile plot of eigenvector components for the Erdös–Rényi case with $n=50$ nodes and edge probability $p=0.5$