{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:58Z","timestamp":1760241718435,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,18]],"date-time":"2018-07-18T00:00:00Z","timestamp":1531872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["2015-05299"],"award-info":[{"award-number":["2015-05299"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov\u2013Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity\u2014both theoretical and numerical\u2014with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.<\/jats:p>","DOI":"10.3390\/e20070534","type":"journal-article","created":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T03:50:43Z","timestamp":1531972243000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations"],"prefix":"10.3390","volume":"20","author":[{"given":"Hector","family":"Zenil","sequence":"first","affiliation":[{"name":"Algorithmic Dynamics Lab, Centre for Molecular Medicine, Karolinska Institute, Stockholm 171 77, Sweden"},{"name":"Unit of Computational Medicine, Department of Medicine, Karolinska Institute, Stockholm 171 77, Sweden"},{"name":"Science for Life Laboratory (SciLifeLab), Stockholm 171 77, Sweden"},{"name":"Algorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, Paris 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0949-046X","authenticated-orcid":false,"given":"Narsis","family":"Kiani","sequence":"additional","affiliation":[{"name":"Algorithmic Dynamics Lab, Centre for Molecular Medicine, Karolinska Institute, Stockholm 171 77, Sweden"},{"name":"Unit of Computational Medicine, Department of Medicine, Karolinska Institute, Stockholm 171 77, Sweden"},{"name":"Science for Life Laboratory (SciLifeLab), Stockholm 171 77, Sweden"},{"name":"Algorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, Paris 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jesper","family":"Tegn\u00e9r","sequence":"additional","affiliation":[{"name":"Unit of Computational Medicine, Department of Medicine, Karolinska Institute, Stockholm 171 77, Sweden"},{"name":"Science for Life Laboratory (SciLifeLab), Stockholm 171 77, Sweden"},{"name":"Biological and Environmental Sciences and Engineering Division (BESE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia"},{"name":"Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1021\/ci950077k","article-title":"Correlation of Entropy with Similarity and Symmetry","volume":"36","author":"Lin","year":"1996","journal-title":"J. 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