The simplicity of planar networks

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial orga...

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Bibliographic Details
Published in:Scientific reports 2013-12, Vol.3 (1), p.3495-3495, Article 3495
Main Authors: Viana, Matheus P., Strano, Emanuele, Bordin, Patricia, Barthelemy, Marc
Format: Article
Language:English
Subjects:
639/766/530/2801
639/766/530/2804
Highways
Humanities and Social Sciences
Models, Theoretical
multidisciplinary
Neural Networks (Computer)
Roads & highways
Science
Wings
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Summary:Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on artificial (roads, highways, railways) and natural networks (leaves, slime mould, insect wings) and show that there are fundamental differences in the organization of urban and biological systems, related to their function, navigation or distribution: straight lines are organized hierarchically in biological cases and have random lengths and locations in urban systems. In the case of time evolving networks, the simplicity is able to reveal important structural changes during their evolution.
ISSN:2045-2322
2045-2322
DOI:10.1038/srep03495