Asymptotic absence of poles of Ihara zeta function of large Erdos-Renyi random graphs

Abstract

Using recent results on the concentration of the largest eigenvalue and maximal vertex degree of large random graphs, we show that the infinite sequence of Erd\H os-R\'enyi random graphs $G(n,\rho_n/n)$ such that $\rho_n/\log n$ infinitely increases as $n\to\infty$ verifies a version of the graph theory Riemann Hypothesis.