{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:32:29Z","timestamp":1768725149941,"version":"3.49.0"},"reference-count":103,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T00:00:00Z","timestamp":1754092800000},"content-version":"vor","delay-in-days":37,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["200778"],"award-info":[{"award-number":["200778"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Bipartite graphs, representing two-mode networks, arise in many research fields. These networks have two disjoint node sets representing distinct entity types, for example persons and groups, with edges representing associations between the two entity types. In bipartite graphs, the smallest possible cycle is a cycle of length four, and hence four-cycles are the smallest structure to model closure in such networks. Exponential-family random graph models (ERGMs) are a widely used model for social, and other, networks, including specifically bipartite networks. Existing ERGM terms to model four-cycles in bipartite networks, however, are relatively rarely used. In this work we demonstrate some problems with these existing terms to model four-cycles, and define new ERGM terms to help overcome these problems. The position of the new terms in the ERGM dependence hierarchy, and their interpretation, is discussed. The new terms are demonstrated in simulation experiments, and their application illustrated on a canonical example of an empirical two-mode network.<\/jats:p>","DOI":"10.1093\/comnet\/cnaf017","type":"journal-article","created":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:13:31Z","timestamp":1754154811000},"source":"Crossref","is-referenced-by-count":3,"title":["Improving exponential-family random graph models for bipartite networks"],"prefix":"10.1093","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2442-4743","authenticated-orcid":false,"given":"Alex","family":"Stivala","sequence":"first","affiliation":[{"name":"Institute of Computing, Universit\u00e0 della Svizzera italiana , Via Buffi 13 , Lugano, Ticino 6900,","place":["Switzerland"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Wang","sequence":"additional","affiliation":[{"name":"Centre for Transformative Innovation, Swinburne University of Technology , John Street , Hawthorn VIC 3122,","place":["Australia"]},{"name":"Institute of Computing, Universit\u00e0 della Svizzera italiana , Via Buffi 13 , Lugano, Ticino 6900,","place":["Switzerland"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Lomi","sequence":"additional","affiliation":[{"name":"Universit\u00e0 della Svizzera italiana , Via Buffi 13 , Lugano, Ticino 6900,","place":["Switzerland"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,8,2]]},"reference":[{"key":"2025080213132702500_cnaf017-B1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.2307\/2576011","article-title":"The duality of persons and groups","volume":"53","author":"Breiger","year":"1974","journal-title":"Soc Forces"},{"key":"2025080213132702500_cnaf017-B2","doi-asserted-by":"crossref","first-page":"e0000010","DOI":"10.1371\/journal.pcsy.0000010","article-title":"Pattern detection in bipartite networks: a review of 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