The simplicity of planar networks.

Abstract:

: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.

journal_name

Sci Rep

journal_title

Scientific reports

authors

Viana MP,Strano E,Bordin P,Barthelemy M

doi

10.1038/srep03495

subject

Has Abstract

pub_date

2013-12-13 00:00:00

pages

3495

issn

2045-2322

pii

srep03495

journal_volume

3

pub_type

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