title: Edge anisotropy and the geometric perspective on flow networks.
abstract: Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Nora
authors.initials: N
authors.lastname: Molkenthin
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Hannes
authors.initials: H
authors.lastname: Kutza
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Liubov
authors.initials: L
authors.lastname: Tupikina
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Norbert
authors.identifier: 0000000314377039
authors.initials: N
authors.lastname: Marwan
authors.affiliation: Research Domain I - Earth System Analysis, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Jonathan F
authors.initials: JF
authors.lastname: Donges
authors.affiliation: Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University, Carl-von-Ossietzky-Straße 9, 26129 Oldenburg, Germany.
authors.forename: Ulrike
authors.initials: U
authors.lastname: Feudel
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Jürgen
authors.identifier: 0000000259264276
authors.initials: J
authors.lastname: Kurths
authors.affiliation: Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
authors.forename: Reik V
authors.initials: RV
authors.lastname: Donner