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The group memberships are generated by a bipartite configuration model. The model generalizes the classical random intersection graph model, a special case where each community is a complete graph. The RIGC model is analytically tractable. We prove a phase transition in the size of the largest connected component in terms of the model parameters. We prove that percolation on RIGC produces a graph within the RIGC family, also undergoing a phase transition with respect to size of the largest component. Our proofs rely on the connection to the bipartite configuration model. Our related results on the bipartite configuration model are of independent interest, since they shed light on interesting differences from the unipartite case.<\/jats:p>","DOI":"10.1002\/rsa.21063","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T12:16:14Z","timestamp":1639484174000},"page":"406-461","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Phase transition in random intersection graphs with communities"],"prefix":"10.1002","volume":"60","author":[{"given":"Remco","family":"van der Hofstad","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven The Netherlands"}]},{"given":"J\u00falia","family":"Komj\u00e1thy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Delft University of Technology Delft The Netherlands"}]},{"given":"Vikt\u00f3ria","family":"Vadon","sequence":"additional","affiliation":[{"name":"Institute of Mathematics University of Miskolc Miskolc Hungary"}]}],"member":"311","published-online":{"date-parts":[[2021,12,14]]},"reference":[{"issue":"3","key":"e_1_2_7_2_1","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1214\/18-AIHP926","article-title":"Limit laws for self\u2010loops and multiple edges in the configuration model","volume":"55","author":"Angel O.","year":"2019","journal-title":"Annales de l'Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques"},{"key":"e_1_2_7_3_1","volume-title":"Branching processes","author":"Athreya K. 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