{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:24:29Z","timestamp":1772252669882,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Three computer algorithms are presented. One reduces a network N to its interior, I. Another counts all the triangles in a network, and the last randomly generates networks similar to N given just its interior I. However, these algorithms are not the usual numeric programs that manipulate a matrix representation of the network; they are set-based. Union and meet are essential binary operators; contained_in is the basic relational comparator. The interior I is shown to have desirable formal properties and to provide an effective way of revealing \u201ccommunities\u201d in social networks. A series of networks randomly generated from I is compared with the original network, N.<\/jats:p>","DOI":"10.3390\/a14050153","type":"journal-article","created":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T10:20:36Z","timestamp":1620728436000},"page":"153","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Set-Theoretic Approach to Modeling Network Structure"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3753-9208","authenticated-orcid":false,"given":"John L.","family":"Pfaltz","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Virginia, Charlottesville, VA 22911, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,11]]},"reference":[{"key":"ref_1","unstructured":"Agnarsson, G., and Greenlaw, R. (2007). 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