{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:41:09Z","timestamp":1761709269571,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,10,31]],"date-time":"2016-10-31T00:00:00Z","timestamp":1477872000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Railway networks are among the many physical systems that reveal a fractal structure. This paper studies the Portuguese railway system, and analyzes how it evolved over time, namely what concerns the structure of its different levels, and its distribution over the territory. Different mathematical tools are adopted, such as fractal dimension, entropy and state space portrait. The results are consistent with the historical evolution of the network.<\/jats:p>","DOI":"10.3390\/e18110388","type":"journal-article","created":{"date-parts":[[2016,10,31]],"date-time":"2016-10-31T11:09:46Z","timestamp":1477912186000},"page":"388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Entropy Analysis of a Railway Network\u2019s Complexity"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9388-4308","authenticated-orcid":false,"given":"Duarte","family":"Val\u00e9rio","sequence":"first","affiliation":[{"name":"IDMEC, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Lopes","sequence":"additional","affiliation":[{"name":"UISPA - LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"Jos\u00e9","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1111\/j.1538-4632.1991.tb00245.x","article-title":"Is the suburban railway system a fractal?","volume":"23","author":"Benguigui","year":"1991","journal-title":"Geogr. 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