{"id":5573,"date":"2025-08-20T20:53:16","date_gmt":"2025-08-20T20:53:16","guid":{"rendered":"https:\/\/cricca.disi.unitn.it\/montresor\/?page_id=5573"},"modified":"2025-08-20T20:53:27","modified_gmt":"2025-08-20T20:53:27","slug":"higher-order-networks-and-hypergraphs","status":"publish","type":"page","link":"http:\/\/cricca.disi.unitn.it\/montresor\/research\/topics\/higher-order-networks-and-hypergraphs\/","title":{"rendered":"Higher-Order Networks and Hypergraphs"},"content":{"rendered":"<p data-start=\"250\" data-end=\"741\">Traditional net\u00adwork models cap\u00adtu\u00adre pair\u00adwi\u00adse inte\u00adrac\u00adtions bet\u00adween enti\u00adties, but many real-world systems invol\u00adve group inte\u00adrac\u00adtions that go beyond sim\u00adple edges. Examples ran\u00adge from scien\u00adti\u00adfic col\u00adla\u00adbo\u00adra\u00adtions with mul\u00adti\u00adple co-authors, to bio\u00adche\u00admi\u00adcal reac\u00adtions invol\u00adving seve\u00adral mole\u00adcu\u00adles, to group con\u00adver\u00adsa\u00adtions in social set\u00adtings. These <strong data-start=\"584\" data-end=\"613\">higher-order inte\u00adrac\u00adtions<\/strong> are natu\u00adral\u00adly mode\u00adled with <strong data-start=\"641\" data-end=\"656\">hyper\u00adgra\u00adphs<\/strong> and rela\u00adted struc\u00adtu\u00adres, which extend net\u00adwork scien\u00adce beyond the pair\u00adwi\u00adse paradigm.<\/p>\n<p data-start=\"743\" data-end=\"975\">In col\u00adla\u00adbo\u00adra\u00adtion with <strong data-start=\"765\" data-end=\"785\">Francesco Lotito<\/strong> (PhD, University of Trento, co-advi\u00adsed with <strong>Federico Battiston<\/strong>), we have con\u00adtri\u00adbu\u00adted to the metho\u00addo\u00adlo\u00adgi\u00adcal foun\u00adda\u00adtions of higher-order net\u00adwork ana\u00adly\u00adsis. Our work spans seve\u00adral directions:<\/p>\n<ul data-start=\"977\" data-end=\"1754\">\n<li data-start=\"977\" data-end=\"1171\">\n<p data-start=\"979\" data-end=\"1171\"><strong data-start=\"979\" data-end=\"1013\">Motif ana\u00adly\u00adsis in hyper\u00adgra\u00adphs.<\/strong> We deve\u00adlo\u00adped exact and sam\u00adpling algo\u00adri\u00adthms to detect over\u00adre\u00adpre\u00adsen\u00adted pat\u00adterns of higher-order inte\u00adrac\u00adtions, exten\u00adding the clas\u00adsic notion of net\u00adwork motifs [<a href=\"https:\/\/www.nature.com\/articles\/s42005-022-00858-7\"><span class=\"caps\">CP22<\/span><\/a>] [<a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00607-023-01230-5\"><span class=\"caps\">SC24<\/span><\/a>] .<\/p>\n<\/li>\n<li data-start=\"1172\" data-end=\"1341\">\n<p data-start=\"1174\" data-end=\"1341\"><strong data-start=\"1174\" data-end=\"1200\">Hyperlink com\u00admu\u00adni\u00adties.<\/strong> We intro\u00addu\u00adced a fra\u00admework to unco\u00adver meso\u00adsca\u00adle struc\u00adtu\u00adres in hyper\u00adgra\u00adphs, cap\u00adtu\u00adring hie\u00adrar\u00adchi\u00adcal orga\u00adni\u00adza\u00adtion and over\u00adlap\u00adping com\u00admu\u00adni\u00adties [<a href=\"https:\/\/arxiv.org\/pdf\/2303.01385.pdf\"><span class=\"caps\">CN24<\/span><\/a>].<\/p>\n<\/li>\n<li data-start=\"1342\" data-end=\"1532\">\n<p data-start=\"1344\" data-end=\"1532\"><strong data-start=\"1344\" data-end=\"1383\">Directed and mul\u00adti\u00adplex hyper\u00adgra\u00adphs.<\/strong> We pro\u00adpo\u00adsed mea\u00adsu\u00adres for reci\u00adpro\u00adci\u00adty, motif ana\u00adly\u00adsis, and mul\u00adti\u00adlayer con\u00adnec\u00adti\u00advi\u00adty in systems with direc\u00adted or mul\u00adti\u00adplex higher-order interactions.<\/p>\n<\/li>\n<li data-start=\"1533\" data-end=\"1754\">\n<p data-start=\"1535\" data-end=\"1754\"><strong data-start=\"1535\" data-end=\"1557\">Software and data.<\/strong> We crea\u00adted <strong data-start=\"1569\" data-end=\"1584\">Hypergraphx<\/strong>, one of the lea\u00adding Python libra\u00adries for higher-order net\u00adwork ana\u00adly\u00adsis, and con\u00adtri\u00adbu\u00adted to <strong data-start=\"1676\" data-end=\"1695\">Hypergraph-data<\/strong>, a cura\u00adted repo\u00adsi\u00adto\u00adry of real-world hyper\u00adgra\u00adph data\u00adse\u00adts [<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2303.15356\"><span class=\"caps\">JCN23<\/span><\/a>] .<\/p>\n<\/li>\n<\/ul>\n<hr>\n<p data-start=\"1756\" data-end=\"2135\">[<span class=\"caps\">CP22<\/span>]&nbsp;&nbsp;&nbsp;Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, and Federico Battiston. Higher-order motif ana\u00adly\u00adsis in hyper\u00adgra\u00adphs. <em>Communications Physics<\/em>, 5(1):79, 2022.&nbsp;<span class=\"caps\">ISBN<\/span>&nbsp;2399\u20133650.&nbsp;<a href=\"https:\/\/www.nature.com\/articles\/s42005-022-00858-7\">[<span class=\"caps\">PDF<\/span>]<\/a>,&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/refs\/lotito22.bib\">[Bibtex]<\/a>.<\/p>\n<p data-start=\"1756\" data-end=\"2135\">[<span class=\"caps\">JCN23<\/span>]&nbsp;&nbsp;&nbsp;Quintino Francesco Lotito, Martina Contisciani, Caterina De Bacco, Leonardo Di Gaetano, Luca Gallo, Alberto Montresor, Federico Musciotto, Nicol\u00f2 Ruggeri, and Federico Battiston. Hypergraphx: a libra\u00adry for higher-order net\u00adwork ana\u00adly\u00adsis. <em>Journal of Complex Networks<\/em>, 11(3), May 2023.&nbsp;<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2303.15356\">[<span class=\"caps\">PDF<\/span>]<\/a>,&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/refs\/hypergraphx23.bib\">[Bibtex]<\/a>.<\/p>\n<p data-start=\"1756\" data-end=\"2135\">[<span class=\"caps\">SC24<\/span>]&nbsp; &nbsp;Quintino Francesco Lotito, Federico Musciotto, Federico Battiston, and Alberto Montresor. Exact and sam\u00adpling methods for mining higher-order motifs in lar\u00adge hyper\u00adgra\u00adphs. <em>Springer Computing<\/em>, pages 475\u2013494, February 2024.&nbsp;<a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00607-023-01230-5\">[<span class=\"caps\">PDF<\/span>]<\/a>,&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/refs\/springercomputing24.bib\">[Bibtex]<\/a>.<\/p>\n<p data-start=\"1756\" data-end=\"2135\">[<span class=\"caps\">CN24<\/span>]&nbsp;&nbsp;&nbsp;Quintino Francesco Lotito, Federico Musciotto, Alberto Montresor, and Federico Battiston. Hyperlink com\u00admu\u00adni\u00adties in higher-order net\u00adworks. <em>J. Complex Networks<\/em>, 12(2), April 2024.&nbsp;<a href=\"https:\/\/arxiv.org\/pdf\/2303.01385.pdf\">[<span class=\"caps\">PDF<\/span>]<\/a>,&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/refs\/lotito2024hyperlink.bib\">[Bibtex]<\/a>.<\/p>\n<p data-start=\"1756\" data-end=\"2135\">[<span class=\"caps\">ANS24<\/span>]&nbsp;&nbsp;&nbsp;Quintino Francesco Lotito, Alberto Montresor, and Federico Battiston. Multiplex mea\u00adsu\u00adres for higher-order net\u00adworks. <em>Applied Network Science<\/em>, 9(55), September 2024.&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/papers\/2024-ASN.pdf\">[<span class=\"caps\">PDF<\/span>]&nbsp;<\/a>,&nbsp;<a href=\"http:\/\/disi.unitn.it\/~montreso\/pubs\/refs\/ANS2024.bib\">[Bibtex]&nbsp;<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Traditional net\u00adwork models cap\u00adtu\u00adre pair\u00adwi\u00adse inte\u00adrac\u00adtions bet\u00adween enti\u00adties, but many real-world systems invol\u00adve group inte\u00adrac\u00adtions that go beyond sim\u00adple edges. Examples ran\u00adge from scien\u00adti\u00adfic col\u00adla\u00adbo\u00adra\u00adtions with mul\u00adti\u00adple co-authors, to bio\u00adche\u00admi\u00adcal reac\u00adtions invol\u00adving seve\u00adral mole\u00adcu\u00adles, to group con\u00adver\u00adsa\u00adtions in social set\u00adtings. These higher-order inte\u00adrac\u00adtions are natu\u00adral\u00adly mode\u00adled with hyper\u00adgra\u00adphs and rela\u00adted struc\u00adtu\u00adres, which extend net\u00adwork science&nbsp;[\u2026]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1394,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"wp_typography_post_enhancements_disabled":false,"footnotes":""},"class_list":["post-5573","page","type-page","status-publish","hentry","post"],"_links":{"self":[{"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/pages\/5573","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/comments?post=5573"}],"version-history":[{"count":1,"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/pages\/5573\/revisions"}],"predecessor-version":[{"id":5575,"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/pages\/5573\/revisions\/5575"}],"up":[{"embeddable":true,"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/pages\/1394"}],"wp:attachment":[{"href":"http:\/\/cricca.disi.unitn.it\/montresor\/wp-json\/wp\/v2\/media?parent=5573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}