{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T14:56:50Z","timestamp":1777733810835,"version":"3.51.4"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"name":"URJC fellowship","award":["PREDOC-21-026-2164"],"award-info":[{"award-number":["PREDOC-21-026-2164"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article, we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data, which we then use for discussion and analysis.<\/jats:p>","DOI":"10.1093\/comnet\/cnae037","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T01:55:54Z","timestamp":1725414954000},"source":"Crossref","is-referenced-by-count":4,"title":["Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8118-6403","authenticated-orcid":false,"given":"Gonzalo","family":"Contreras-Aso","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Ciencia e Ingenier\u00eda de los Materiales y Tecnolog\u00eda Electr\u00f3nica, Universidad Rey Juan Carlos , c\/Tulip\u00e1n s\/n , 28933 M\u00f3stoles (Madrid), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Regino","family":"Criado","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Ciencia e Ingenier\u00eda de los Materiales y Tecnolog\u00eda Electr\u00f3nica, Universidad Rey Juan Carlos , c\/Tulip\u00e1n s\/n , 28933 M\u00f3stoles (Madrid), Spain"},{"name":"Data, Complex Networks and Cybersecurity Research Institute, Universidad Rey Juan Carlos , Plaza Manuel Becerra, 14 28028 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Romance","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Ciencia e Ingenier\u00eda de los Materiales y Tecnolog\u00eda Electr\u00f3nica, Universidad Rey Juan Carlos , c\/Tulip\u00e1n s\/n , 28933 M\u00f3stoles (Madrid), Spain"},{"name":"Data, Complex Networks and Cybersecurity Research Institute, Universidad Rey Juan Carlos , Plaza Manuel Becerra, 14 28028 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"2024091013012912300_cnae037-B1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.chaos.2019.06.017","article-title":"Non-backtracking PageRank: from the classic model to hashimoto matrices","volume":"126","author":"Aleja","year":"2019","journal-title":"Chaos Solitons Fractals"},{"key":"2024091013012912300_cnae037-B2","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.tcs.2016.03.016","article-title":"Directed hypergraphs: introduction and fundamental algorithms\u2014a survey","volume":"658","author":"Ausiello","year":"2017","journal-title":"Theor. 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