{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:24:15Z","timestamp":1777645455196,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2009,10,1]],"date-time":"2009-10-01T00:00:00Z","timestamp":1254355200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2009,10]]},"abstract":"<jats:p>An important problem of knowledge discovery that has recently evolved in various reallife networks is identifying the largest set of vertices that are functionally associated. The topology of many real-life networks shows scale-freeness, where the vertices of the underlying graph follow a power-law degree distribution. Moreover, the graphs corresponding to most of the real-life networks are weighted in nature. In this article, the problem of finding the largest group or association of vertices that are dense (denoted as dense vertexlet) in a weighted scale-free graph is addressed. Density quantifies the degree of similarity within a group of vertices in a graph. The density of a vertexlet is defined in a novel way that ensures significant participation of all the vertices within the vertexlet. It is established that the problem is NP-complete in nature. An upper bound on the order of the largest dense vertexlet of a weighted graph, with respect to certain density threshold value, is also derived. Finally, an O(n $^2$ log n) (n denotes the number of vertices in the graph) heuristic graph mining algorithm that produces an approximate solution for the problem is presented.<\/jats:p>","DOI":"10.3233\/fi-2009-164","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T22:58:08Z","timestamp":1575327488000},"page":"1-25","source":"Crossref","is-referenced-by-count":6,"title":["Mining the Largest Dense Vertexlet in a Weighted Scale-free \t\t\t Graph"],"prefix":"10.1177","volume":"96","author":[{"given":"Sanghamitra","family":"Bandyopadhyay","sequence":"first","affiliation":[{"name":"Machine Intelligence Unit, Indian Statistical Institute,\r\t\t\t 203 B. T. Road, Kolkata - 700108, India. E-mail: {sanghami,malay_r}@isical.ac.in"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Malay","family":"Bhattacharyya","sequence":"additional","affiliation":[{"name":"Machine Intelligence Unit, Indian Statistical Institute,\r\t\t\t 203 B. T. Road, Kolkata - 700108, India. E-mail: {sanghami,malay_r}@isical.ac.in"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,10,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-164","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-164","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:15Z","timestamp":1777444335000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2009-164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["10.3233\/FI-2009-164"],"URL":"https:\/\/doi.org\/10.3233\/fi-2009-164","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10]]}}}