title: 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.
authors: Department of Developmental and Cell Biology, University of California, Irvine, CA 92697, USA.
authors: Matheus P
authors: MP
authors: Viana
authors: Laboratory of Geographic Information Systems (LASIG), School of Architecture, Civil and Environmental Engineering (ENAC), Ecole Polytechnique Fédérale de Lausanne (EPFL).
authors: Emanuele
authors: E
authors: Strano
authors: 1] Université Paris-Est, Institut de Recherche en Constructibilité, ESTP, F-94230, Cachan, France [2] Université Paris Diderot, Sorbonne Paris Cité, Institut des Energies de Demain (IED), 75205 Paris, France.
authors: Patricia
authors: P
authors: Bordin
authors: 1] Institut de Physique Théorique, CEA, CNRS-URA 2306, F-91191, Gif-sur-Yvette, France [2] Centre d'Analyse et de Mathématiques Sociales, EHESS, 130, avenue de France, 75244 Paris.
authors: Marc
authors: M
authors: Barthelemy
mesh_terms: D008962:Models, Theoretical; D016571:Neural Networks, Computer