{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:48:11Z","timestamp":1753876091050,"version":"3.41.2"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T00:00:00Z","timestamp":1737936000000},"content-version":"vor","delay-in-days":29,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP240100872"],"award-info":[{"award-number":["DP240100872"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Large complex networks are often organized into groups or communities. In this paper, we introduce and investigate a generative model of network evolution that reproduces all four pairwise community types that exist in directed networks: assortative, core-periphery, disassortative, and the newly introduced source-basin type. We fix the number of nodes and the community membership of each node, allowing node connectivity to change through rewiring mechanisms that depend on the community membership of the involved nodes. We determine the dependence of the community relationship on the model parameters using a mean-field solution. It reveals that a difference in the swap probabilities of the two communities is a necessary condition to obtain a core-periphery relationship and that a difference in the average in-degree of the communities is a necessary condition for a source-basin relationship. More generally, our analysis reveals multiple possible scenarios for the transition between the different structure types, and sheds light on the mechanisms underlying the observation of the different types of communities in network data.<\/jats:p>","DOI":"10.1093\/comnet\/cnae048","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T17:22:27Z","timestamp":1737998547000},"source":"Crossref","is-referenced-by-count":0,"title":["A generative model for non-assortative communities in directed networks"],"prefix":"10.1093","volume":"13","author":[{"given":"Cathy Xuanchi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics & Centre for Complex Systems, The University of Sydney , Sydney, NSW 2006,","place":["Australia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tristram J","family":"Alexander","sequence":"additional","affiliation":[{"name":"School of Physics & Centre for Complex Systems, The University of Sydney , Sydney, NSW 2006,","place":["Australia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1932-3710","authenticated-orcid":false,"given":"Eduardo G","family":"Altmann","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics & Centre for Complex Systems, The University of Sydney , Sydney, NSW 2006,","place":["Australia"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,1,27]]},"reference":[{"key":"2025012717174941600_cnae048-B1","doi-asserted-by":"crossref","first-page":"7821","DOI":"10.1073\/pnas.122653799","article-title":"Community structure in social and biological networks","volume":"99","author":"Girvan","year":"2002","journal-title":"Proc Natl Acad Sci USA"},{"key":"2025012717174941600_cnae048-B2","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.physrep.2009.11.002","article-title":"Community detection in graphs","volume":"486","author":"Fortunato","year":"2010","journal-title":"Phys Rep"},{"key":"2025012717174941600_cnae048-B3","doi-asserted-by":"crossref","first-page":"8577","DOI":"10.1073\/pnas.0601602103","article-title":"Modularity and community structure in networks","volume":"103","author":"Newman","year":"2006","journal-title":"Proc Natl Acad Sci USA"},{"key":"2025012717174941600_cnae048-B4","doi-asserted-by":"crossref","first-page":"P10008","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","article-title":"Fast unfolding of communities in large networks","volume":"2008","author":"Blondel","year":"2008","journal-title":"J Stat Mech Theory Exp"},{"key":"2025012717174941600_cnae048-B5","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/S0378-8733(99)00019-2","article-title":"Models of core\/periphery structures","volume":"21","author":"Borgatti","year":"2000","journal-title":"Soc 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structure in financial networks","volume":"88","author":"Barucca","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"2025012717174941600_cnae048-B10","doi-asserted-by":"crossref","first-page":"043012","DOI":"10.1088\/1367-2630\/aab547","article-title":"Core-periphery structure requires something else in the network","volume":"20","author":"Kojaku","year":"2018","journal-title":"N J Phys"},{"year":"2018","author":"Betzel","key":"2025012717174941600_cnae048-B11"},{"key":"2025012717174941600_cnae048-B12","doi-asserted-by":"crossref","first-page":"043287","DOI":"10.1103\/PhysRevResearch.5.043287","article-title":"Assortative and preferential attachment lead to core-periphery networks","volume":"5","author":"Ure\u00f1a-Carri\u00f3n","year":"2023","journal-title":"Phys Rev Res"},{"key":"2025012717174941600_cnae048-B13","doi-asserted-by":"crossref","first-page":"pgad364","DOI":"10.1093\/pnasnexus\/pgad364","article-title":"Nonassortative relationships between groups of nodes are 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Repository with codes. Available on GitHub https:\/\/github.com\/communityType\/model and (an archived version) on Zenodo 10.5281\/zenodo.13846866, 2024 (September 2024, date last accessed)."}],"container-title":["Journal of Complex Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/13\/1\/cnae048\/61650531\/cnae048.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/comnet\/article-pdf\/13\/1\/cnae048\/61650531\/cnae048.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T17:22:40Z","timestamp":1737998560000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/comnet\/article\/doi\/10.1093\/comnet\/cnae048\/7984302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,29]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,12,29]]}},"URL":"https:\/\/doi.org\/10.1093\/comnet\/cnae048","relation":{},"ISSN":["2051-1329"],"issn-type":[{"type":"electronic","value":"2051-1329"}],"subject":[],"published-other":{"date-parts":[[2025,2]]},"published":{"date-parts":[[2024,12,29]]},"article-number":"cnae048"}}