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Updated: May 29, 2025

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
Published on: January 11, 2018
Singular-value statistics of directed random graphs
J A Méndez-Bermúdez1, R Aguilar-Sánchez2
1Universidad Nacional Autónoma de Honduras, Benemérita Universidad Autónoma de Puebla, Instituto de Física, Puebla 72570, Mexico and Escuela de Física, Facultad de Ciencias, Honduras.
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.
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