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Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far.<\/jats:p>\n          <jats:p>\n            As a first step in this direction, in this work, we study the problem of\n            <jats:italic>core decomposition of a multilayer network<\/jats:italic>\n            . Unlike the single-layer counterpart in which cores are all nested into one another and can be computed in linear time, the multilayer context is much more challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting, we devise three algorithms, which differ in the way they visit the core lattice and in their pruning techniques. We assess time and space efficiency of the three algorithms on a large variety of real-world multilayer networks.\n          <\/jats:p>\n          <jats:p>\n            We then move a step forward and study the problem of extracting the\n            <jats:italic>inner-most<\/jats:italic>\n            (also known as\n            <jats:italic>maximal<\/jats:italic>\n            ) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. This allows for a consistent speed up over a na\u00efve method that simply filters out non-inner-most ones from all the cores.\n          <\/jats:p>\n          <jats:p>\n            Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of\n            <jats:italic>densest-subgraph extraction in multilayer networks<\/jats:italic>\n            . We introduce a definition of multilayer densest subgraph that tradesoff between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of\n            <jats:italic>frequent cross-graph quasi-cliques<\/jats:italic>\n            and to generalize the\n            <jats:italic>community-search<\/jats:italic>\n            problem to the multilayer setting.\n          <\/jats:p>","DOI":"10.1145\/3369872","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T14:54:43Z","timestamp":1580741683000},"page":"1-40","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":47,"title":["Core Decomposition in Multilayer Networks"],"prefix":"10.1145","volume":"14","author":[{"given":"Edoardo","family":"Galimberti","sequence":"first","affiliation":[{"name":"ISI Foundation and University of Turin, Torino, Italy"}]},{"given":"Francesco","family":"Bonchi","sequence":"additional","affiliation":[{"name":"ISI Foundation and Eurecat, Torino, Italy"}]},{"given":"Francesco","family":"Gullo","sequence":"additional","affiliation":[{"name":"UniCredit, Rome, Italy"}]},{"given":"Tommaso","family":"Lanciano","sequence":"additional","affiliation":[{"name":"Sapienza University of Rome, Roma, Italy"}]}],"member":"320","published-online":{"date-parts":[[2020,2,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972832.5"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2013.2297918"},{"key":"e_1_2_1_3_1","volume-title":"Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS\u201905)","author":"Alvarez-Hamelin J. 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