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The embeddings that we are looking at aim to keep vertices that are grouped in communities together and keep the rest apart. To achieve this property, we utilize coarsening that respects possible community structures of the given graph. We employ a hierarchical multilevel coarsening approach that identifies communities (strongly connected groups of vertices) at every level. The multilevel strategy allows any given (presumably expensive) graph embedding algorithm to be made into a more scalable (and faster) algorithm. We demonstrate the presented approach on a number of given embedding algorithms and large\u2010scale graphs and achieve speed\u2010up over the methods in a recent paper.<\/jats:p>","DOI":"10.1002\/nla.2326","type":"journal-article","created":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T14:58:35Z","timestamp":1600873115000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multilevel graph embedding"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-6922-9706","authenticated-orcid":false,"given":"Benjamin","family":"Quiring","sequence":"first","affiliation":[{"name":"Computer Science Department Northeastern University Boston Massachusetts USA"}]},{"given":"Panayot S.","family":"Vassilevski","sequence":"additional","affiliation":[{"name":"Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore California USA"},{"name":"Fariborz Maseeh Department of Mathematics and Statistics Portland State University Portland Oregon USA"}]}],"member":"311","published-online":{"date-parts":[[2020,9,23]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238511"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/050626272"},{"key":"e_1_2_9_5_1","first-page":"123","article-title":"An aggregation\u2010based algebraic multigrid method","volume":"37","author":"Notay Y","year":"2010","journal-title":"Electron Trans Numer Anal"},{"issue":"4","key":"e_1_2_9_6_1","first-page":"39","article-title":"BootCMatch: a software package for bootstrap AMG based on graph weighted matching","volume":"44","author":"D'Ambra P","year":"2018","journal-title":"ACM Trans Math Softw"},{"key":"e_1_2_9_7_1","unstructured":"QuiringB VassilevskiPS. 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