{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:45:35Z","timestamp":1760402735373,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T00:00:00Z","timestamp":1578268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem has potential applications to the development of solutions for secure data transfer on the internet.<\/jats:p>","DOI":"10.3390\/sym12010105","type":"journal-article","created":{"date-parts":[[2020,1,6]],"date-time":"2020-01-06T10:34:46Z","timestamp":1578306886000},"page":"105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Gromov Hyperbolicity in Directed Graphs"],"prefix":"10.3390","volume":"12","author":[{"given":"Ana","family":"Portilla","sequence":"first","affiliation":[{"name":"Math and Computer Science Department, St. Louis University (Madrid Campus), Avenida del Valle 34, 28003 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2851-7442","authenticated-orcid":false,"given":"Jos\u00e9 M.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan\u00e9s, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9 M.","family":"Sigarreta","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico"},{"name":"Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Guerrero, Carlos E. 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