The simplicity of planar networks

Scientific Reports
Matheus P VianaMarc Barthelemy

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.

References

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Citations

Dec 1, 2017·Nature Communications·Ruiqi LiH Eugene Stanley
Dec 22, 2017·Nature Communications·Minjin LeeGourab Ghoshal
Mar 19, 2016·Science Advances·Riccardo GallottiMarc Barthelemy
Feb 18, 2017·Physical Review. E·Sara Najem
Jun 29, 2017·Scientific Reports·Carlos MolineroElsa Arcaute
May 17, 2017·Physical Review. E·Benjamin Lion, Marc Barthelemy
Jan 20, 2018·Physical Review. E·Carlos Gómez-Rodríguez, Ramon Ferrer-I-Cancho
Mar 16, 2019·Algorithmica·Eleftherios AnastasiadisJinshan Zhang

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