{"title":"Singular-value statistics of directed random graphs.","authors":"J A Méndez-Bermúdez, R Aguilar-Sánchez","doi":"10.1103/PhysRevE.110.064307","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"110 6-1","pages":"064307"},"PeriodicalIF":2.2000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.064307","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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