{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:57:58Z","timestamp":1760151478453,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,11]],"date-time":"2022-03-11T00:00:00Z","timestamp":1646956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001117","12001118"],"award-info":[{"award-number":["12001117","12001118"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2016A030313686,","2018A030313267"],"award-info":[{"award-number":["2016A030313686,","2018A030313267"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we propose a random mixed graph model Gn(p(n),q(n)) that incorporates both the classical Erd\u0151s-R\u00e9nyi\u2019s random graph model and the random oriented graph model. We show that the empirical spectral distribution of Gn(p(n),q(n)) converges to the standard semicircle law under some mild condition, and the Monte Carlo simulation highly agrees with our result.<\/jats:p>","DOI":"10.3390\/axioms11030126","type":"journal-article","created":{"date-parts":[[2022,3,11]],"date-time":"2022-03-11T12:58:36Z","timestamp":1647003516000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Spectral Distribution of Random Mixed Graphs"],"prefix":"10.3390","volume":"11","author":[{"given":"Yue","family":"Guan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"given":"Bo","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5212-6578","authenticated-orcid":false,"given":"Minfeng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"given":"Meili","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"given":"Jianxi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"given":"Jinxun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5204-8060","authenticated-orcid":false,"given":"Chao","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]},{"given":"Li","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,11]]},"reference":[{"key":"ref_1","unstructured":"Cvetkovi\u0107, D., Doob, M., and Sachs, H. (1995). Spectra of Graphs, Johann Ambrosius Barth. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bollob\u00e1s, B. (2001). Random Graphs, Cambridge University Press. Number 73.","DOI":"10.1017\/CBO9780511814068"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4547","DOI":"10.1016\/j.laa.2013.02.007","article-title":"The skew energy of random oriented graphs","volume":"438","author":"Chen","year":"2013","journal-title":"Linear Algebra Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.laa.2017.01.011","article-title":"The spectral distribution of random mixed graphs","volume":"519","author":"Hu","year":"2017","journal-title":"Linear Algebra Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"845","DOI":"10.2307\/1427715","article-title":"Giant components in three-parameter random directed graphs","volume":"24","author":"Cohen","year":"1992","journal-title":"Adv. Appl. Probab."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.laa.2014.10.028","article-title":"Hermitian-adjacency matrices and hermitian energies of mixed graphs","volume":"466","author":"Liu","year":"2015","journal-title":"Linear Algebra Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/jgt.22057","article-title":"Hermitian adjacency matrix of digraphs and mixed graphs","volume":"85","author":"Guo","year":"2017","journal-title":"J. Graph Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"548","DOI":"10.2307\/1970079","article-title":"Characteristic vectors of bordered matrices with infinite dimensions","volume":"62","author":"Wigner","year":"1955","journal-title":"Ann. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bai, Z., and Silverstein, J.W. (2010). 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Lectures from the 36th Probability Summer School held in Saint-Flour, 2006.","DOI":"10.1007\/978-3-540-69897-5"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1002\/rsa.20406","article-title":"Sparse random graphs: Eigenvalues and eigenvectors","volume":"42","author":"Tran","year":"2013","journal-title":"Random Struct. 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