Spectral analysis reveals log-periodic leading eigenvalues in scale-invariant random graphs, highlighting discrete self-similarity in complex network structures.
Key Points
To determine the behavior of the leading eigenvalues and eigenvectors of the adjacency matrix in random graph models invariant under node aggregation.
Constructed annealed random graphs of n nodes endowed with Pareto(α)-distributed fitness parameters where 0 < α < 1.
Analytically solved for the leading spectral properties of the network adjacency matrix using the Gamma function in the complex plane.
Leading eigenvalues scale at order √n, alternate in sign, and align at the intersections between the real axis and an analytical logarithmic spiral.