The spectral distribution of random mixed graphs

Dan Hu; Xueliang Li; Xiaogang Liu; Shenggui Zhang

doi:10.1016/j.laa.2017.01.011

The spectral distribution of random mixed graphs

Dan Hu, Xueliang Li, Xiaogang Liu, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ₁(G),λ₂(G),…,λ_n(G) the eigenvalues of H(G). The Hermitian energy of G is defined as E_H(G)=∑_i=1ⁿ|λ_i(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all mixed graphs.

Original language	English
Pages (from-to)	343-365
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	519
DOIs	https://doi.org/10.1016/j.laa.2017.01.011
State	Published - 15 Apr 2017

Keywords

Empirical spectral distribution
Hermitian energy
Limiting spectral distribution
Random mixed graphs

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abstract = "Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ1(G),λ2(G),…,λn(G) the eigenvalues of H(G). The Hermitian energy of G is defined as EH(G)=∑i=1n|λi(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all mixed graphs.",

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author = "Dan Hu and Xueliang Li and Xiaogang Liu and Shenggui Zhang",

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T1 - The spectral distribution of random mixed graphs

AU - Hu, Dan

AU - Li, Xueliang

AU - Liu, Xiaogang

AU - Zhang, Shenggui

PY - 2017/4/15

Y1 - 2017/4/15

N2 - Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ1(G),λ2(G),…,λn(G) the eigenvalues of H(G). The Hermitian energy of G is defined as EH(G)=∑i=1n|λi(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all mixed graphs.

AB - Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ1(G),λ2(G),…,λn(G) the eigenvalues of H(G). The Hermitian energy of G is defined as EH(G)=∑i=1n|λi(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all mixed graphs.

KW - Empirical spectral distribution

KW - Hermitian energy

KW - Limiting spectral distribution

KW - Random mixed graphs

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U2 - 10.1016/j.laa.2017.01.011

DO - 10.1016/j.laa.2017.01.011

M3 - 文章

AN - SCOPUS:85010217260

SN - 0024-3795

VL - 519

SP - 343

EP - 365

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The spectral distribution of random mixed graphs

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Keywords

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