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We also study the analogous problem for quasiconvex functions and obtain a characterization of the largest quasiconvex function that is below a given datum.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/nhm.2021019","type":"journal-article","created":{"date-parts":[[2021,6,30]],"date-time":"2021-06-30T07:58:03Z","timestamp":1625039883000},"page":"591","source":"Crossref","is-referenced-by-count":1,"title":["Convex and quasiconvex functions in metric graphs"],"prefix":"10.3934","volume":"16","author":[{"given":"Leandro M. Del","family":"Pezzo","sequence":"first","affiliation":[]},{"given":"Nicol\u00e1s","family":"Frevenza","sequence":"additional","affiliation":[]},{"given":"Julio D.","family":"Rossi","sequence":"additional","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2021019-1","doi-asserted-by":"publisher","unstructured":"B. Abbasi, A. M. Oberman.A partial differential equation for the $ \\epsilon $-uniformly quasiconvex envelope, <i>IMA J. Numer. 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