{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:37Z","timestamp":1760242837722,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,12,25]],"date-time":"2016-12-25T00:00:00Z","timestamp":1482624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CAPES (STIC-AmSud)"},{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004809","name":"FINEP","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"FAPERJ","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011875","name":"MCTIC","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100011875","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.<\/jats:p>","DOI":"10.3390\/a10010001","type":"journal-article","created":{"date-parts":[[2016,12,28]],"date-time":"2016-12-28T11:22:14Z","timestamp":1482924134000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["MultiAspect Graphs: Algebraic Representation and Algorithms"],"prefix":"10.3390","volume":"10","author":[{"given":"Klaus","family":"Wehmuth","sequence":"first","affiliation":[{"name":"National Laboratory for Scientific Computing (LNCC), Av. Get\u00falio Vargas 333, 25651-075 Petr\u00f3polis, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c9ric","family":"Fleury","sequence":"additional","affiliation":[{"name":"Institut national de recherche en informatique et en automatique (INRIA), Centre national de la recherche scientifique (CNRS), Universit\u00e9 de Lyon, \u00c9cole normale sup\u00e9rieure de Lyon, UCB Lyon 1, LIP UMR 5668, F-69342, 46, Alle\u00e9 d\u2019Italie, 69364 Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Artur","family":"Ziviani","sequence":"additional","affiliation":[{"name":"National Laboratory for Scientific Computing (LNCC), Av. Get\u00falio Vargas 333, 25651-075 Petr\u00f3polis, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,25]]},"reference":[{"key":"ref_1","unstructured":"Distel, R. (2010). Graph Theory, Springer. 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