{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:47:00Z","timestamp":1753876020311,"version":"3.41.2"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T00:00:00Z","timestamp":1661212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,23]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article introduces Haros graphs, a construction which provides a graph-theoretical representation of real numbers in the unit interval reached via paths in the Farey binary tree. We show how the topological structure of Haros graphs yields a natural classification of the real numbers into a hierarchy of families. To unveil such classification, we introduce an entropic functional on these graphs and show that it can be expressed, thanks to its fractal nature, in terms of a generalized de Rham curve. We show that this entropy reaches a global maximum at the reciprocal of the Golden number and otherwise displays a rich hierarchy of local maxima and minima that relate to specific families of irrationals (noble numbers) and rationals, overall providing an exotic classification and representation of the reals numbers according to entropic principles. We close the article with a number of conjectures and outline a research programme on Haros graphs.<\/jats:p>","DOI":"10.1093\/comnet\/cnac043","type":"journal-article","created":{"date-parts":[[2022,9,15]],"date-time":"2022-09-15T06:13:56Z","timestamp":1663222436000},"source":"Crossref","is-referenced-by-count":3,"title":["Haros graphs: an exotic representation of real numbers"],"prefix":"10.1093","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8701-6253","authenticated-orcid":false,"given":"Jorge","family":"Calero-Sanz","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Aeroespacial, ETSIAE, Universidad Polit\u00e9cnica de Madrid , 28040 Madrid, Spain and Signal and Communications Theory and Telematic Systems and Computing, Rey Juan Carlos University, 28942, Fuenlabrada, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bartolo","family":"Luque","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de Madrid Departamento de Matem\u00e1tica Aplicada a la Ingenier\u00eda Aeroespacial, ETSIAE, , 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Lacasa","sequence":"additional","affiliation":[{"name":"Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB), E-07122, Palma de Mallorca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,9,15]]},"reference":[{"key":"2022092708490738800_B1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780199219858.001.0001","volume-title":"An Introduction to the Theory of Numbers","author":"Hardy,","year":"2008","edition":"6th edn"},{"key":"2022092708490738800_B2","volume-title":"Concrete Mathematics: A Foundation for Computer Science","author":"Graham,","year":"1994","edition":"2nd edn"},{"volume-title":"Irrationality and Transcendence in Number Theory","year":"2022","author":"Angell,","key":"2022092708490738800_B3"},{"key":"2022092708490738800_B4","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.jda.2005.03.007","article-title":"Exact arithmetic on the Stern-Brocot tree","volume":"5","author":"Niqui,","year":"2007","journal-title":"J. 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