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Entropy 2016, 18(11), 388;

Entropy Analysis of a Railway Network’s Complexity

IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
UISPA - LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Kevin H. Knuth and Adom Giffin
Received: 12 August 2016 / Revised: 25 October 2016 / Accepted: 27 October 2016 / Published: 31 October 2016
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [1435 KB, uploaded 31 October 2016]   |  


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. View Full-Text
Keywords: railway network; entropy; fractal dimension; fractional calculus railway network; entropy; fractal dimension; fractional calculus

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Valério, D.; Lopes, A.M.; Tenreiro Machado, J.A. Entropy Analysis of a Railway Network’s Complexity. Entropy 2016, 18, 388.

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