乐胖代购免代理版

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The first problem seeks to add edges to enforce that a desired partition is one partition that maximizes modularity. The second problem seeks to find the sparsest representation of a network that has the same partition with maximum modularity as the original network. We present integer programming formulations, a row generation algorithm, and heuristic algorithms to solve these problems. Further, we demonstrate a counter\u2010intuitive behavior of modularity that makes the development of heuristics for general networks difficult. We then present results on a selection of social and illicit networks from the literature.<\/jats:p>","DOI":"10.1002\/net.22084","type":"journal-article","created":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T08:23:02Z","timestamp":1638433382000},"page":"152-177","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimizing edge sets in networks to produce ground truth communities based on modularity"],"prefix":"10.1002","volume":"80","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-8030-0323","authenticated-orcid":false,"given":"Daniel","family":"Kosmas","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5087-4679","authenticated-orcid":false,"given":"John E.","family":"Mitchell","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy New York USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6210-9448","authenticated-orcid":false,"given":"Thomas C.","family":"Sharkey","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering Clemson University Clemson South Carolina USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0307-6743","authenticated-orcid":false,"given":"Boleslaw K.","family":"Szymanski","sequence":"additional","affiliation":[{"name":"Department of Computer Science Rensselaer Polytechnic Institute Troy New York USA"},{"name":"Spo\u0142eczna Akademia Nauk \u0141\u00f3d\u017a Poland"}]}],"member":"311","published-online":{"date-parts":[[2021,12]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2008-00425-1"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.82.046112"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/24725854.2021.1939466"},{"key":"e_1_2_9_5_1","doi-asserted-by":"crossref","unstructured":"A.Bahulkar B. 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