Singular-value statistics of directed random graphs

Physical review. E, vol. 110, pp. 064307

Abstract

Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum 4, 040312 (2023)2691-339910.1103/PRXQuantum.4.040312]. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices A of directed random graphs, where A are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random geometric graphs. Specifically, we focus on the singular-value-spacing ratio r and the minimum singular value λ_{min}. We show that 〈r〉 (where 〈·〉 represents ensemble average) can effectively characterize the crossover between mostly isolated vertices to almost complete graphs, while the probability density function of λ_{min} can clearly distinguish between different graph models.

Authors 2

1. Jose Antonio Mendez-Bermudez

   Benemérita Universidad Autónoma de Puebla · National Autonomous University of Honduras

   Affiliation as printed

   Benemérita Universidad Autónoma de Puebla

   Universidad Nacional Autónoma de Honduras

2. Rocio Aguilar-Sánchez Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University