{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T00:26:31Z","timestamp":1774743991680,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T00:00:00Z","timestamp":1696204800000},"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>Among the various generalizations of persistent topology, that based on rank functions and leading to indexing-aware functions appears to be particularly suited to catching graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies \u201csimple\u201d and \u201csingle-vertex\u201d features in directed and undirected graphs, through which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the \u201csink\u201d feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.<\/jats:p>","DOI":"10.3390\/a16100465","type":"journal-article","created":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T11:56:49Z","timestamp":1696247809000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Exploring Graph and Digraph Persistence"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3732-3108","authenticated-orcid":false,"given":"Mattia G.","family":"Bergomi","sequence":"first","affiliation":[{"name":"Independent Researcher, 20124 Milan, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7973-9734","authenticated-orcid":false,"given":"Massimo","family":"Ferri","sequence":"additional","affiliation":[{"name":"Advanced Research Center on Electronic Systems (ARCES), Department of Mathematics, University of Bologna, 40126 Bologna, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjds\/s13688-017-0109-5","article-title":"A roadmap for the computation of persistent homology","volume":"6","author":"Otter","year":"2017","journal-title":"EPJ Data Sci."},{"key":"ref_2","unstructured":"Mitchell, J.S.B., and Rote, G. 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