Singular-value statistics of directed random graphs.
basic_science · Level V
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- Record sourced from PubMed, PMID 39916267.
- Also identified by DOI 10.1103/PhysRevE.110.064307.
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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.