Edge anisotropy and the geometric perspective on flow networks

Nora Molkenthin, Hannes Kutza, Liubov Tupikina, Norbert Marwan, Jonathan F. Donges, Ulrike Feudel, Jürgen Kurths, Reik V. Donner

Research output: Contribution to journalArticle

4 Citations (Scopus)
3 Downloads (Pure)

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 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.
Original languageEnglish
Article number035802
JournalChaos
Volume27
Issue number3
Early online date22 Feb 2017
DOIs
Publication statusPublished - 2017

Fingerprint

Flow Network
Anisotropy
Geophysical Flows
Spatial Networks
Spatio-temporal Data
anisotropy
Flow structure
Spatial Distribution
Spatial distribution
Metric space
apexes
Alignment
Quantify
Scalar
metric space
Geometry
Vertex of a graph
Demonstrate
spatial distribution
alignment

Keywords

  • physics.flu-dyn
  • nlin.CD
  • anisotropy

Cite this

Molkenthin, N., Kutza, H., Tupikina, L., Marwan, N., Donges, J. F., Feudel, U., ... Donner, R. V. (2017). Edge anisotropy and the geometric perspective on flow networks. Chaos, 27(3), [035802]. https://doi.org/10.1063/1.4971785

Edge anisotropy and the geometric perspective on flow networks. / Molkenthin, Nora; Kutza, Hannes; Tupikina, Liubov; Marwan, Norbert; Donges, Jonathan F.; Feudel, Ulrike; Kurths, Jürgen; Donner, Reik V.

In: Chaos, Vol. 27, No. 3, 035802, 2017.

Research output: Contribution to journalArticle

Molkenthin, N, Kutza, H, Tupikina, L, Marwan, N, Donges, JF, Feudel, U, Kurths, J & Donner, RV 2017, 'Edge anisotropy and the geometric perspective on flow networks', Chaos, vol. 27, no. 3, 035802. https://doi.org/10.1063/1.4971785
Molkenthin N, Kutza H, Tupikina L, Marwan N, Donges JF, Feudel U et al. Edge anisotropy and the geometric perspective on flow networks. Chaos. 2017;27(3). 035802. https://doi.org/10.1063/1.4971785
Molkenthin, Nora ; Kutza, Hannes ; Tupikina, Liubov ; Marwan, Norbert ; Donges, Jonathan F. ; Feudel, Ulrike ; Kurths, Jürgen ; Donner, Reik V. / Edge anisotropy and the geometric perspective on flow networks. In: Chaos. 2017 ; Vol. 27, No. 3.
@article{8dab9c9a4bcc4697aae6211300564843,
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 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.",
keywords = "physics.flu-dyn, nlin.CD, anisotropy",
author = "Nora Molkenthin and Hannes Kutza and Liubov Tupikina and Norbert Marwan and Donges, {Jonathan F.} and Ulrike Feudel and J{\"u}rgen Kurths and Donner, {Reik V.}",
note = "ACKNOWLEDGMENTS This work was financially supported by the German Research Foundation (DFG) via the DFG Graduate School 1536 (“Visibility and Visualization”), the European Commission via the Marie-Curie ITN LINC (P7-PEOPLE-2011-ITN, Grant No. 289447), the German Federal Ministry for Education and Research (BMBF) via the BMBF Young Investigator's Group CoSy-CC2 (“Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change, Grant No. 01LN1306A”) and the project GLUES, the Stordalen Foundation (via the Planetary Boundary Research Network PB.net), the Earth League's EarthDoc program, and the Volkswagen Foundation via the project “Recurrent extreme events in spatially extended excitable systems: Mechanism of their generation and termination” (Grant No. 85391). The presented research has greatly benefited from discussions with Emilio Hern{\'a}ndez-Garcia and Crist{\'o}bal L{\'o}pez. Parts of the network calculations have been performed using the Python package pyunicorn56 (see http://tocsy.pik-potsdam.de/pyunicorn.php). pyunicorn is freely available for download at https://github.com/pik-copan/pyunicorn",
year = "2017",
doi = "10.1063/1.4971785",
language = "English",
volume = "27",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics",
number = "3",

}

TY - JOUR

T1 - Edge anisotropy and the geometric perspective on flow networks

AU - Molkenthin, Nora

AU - Kutza, Hannes

AU - Tupikina, Liubov

AU - Marwan, Norbert

AU - Donges, Jonathan F.

AU - Feudel, Ulrike

AU - Kurths, Jürgen

AU - Donner, Reik V.

N1 - ACKNOWLEDGMENTS This work was financially supported by the German Research Foundation (DFG) via the DFG Graduate School 1536 (“Visibility and Visualization”), the European Commission via the Marie-Curie ITN LINC (P7-PEOPLE-2011-ITN, Grant No. 289447), the German Federal Ministry for Education and Research (BMBF) via the BMBF Young Investigator's Group CoSy-CC2 (“Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change, Grant No. 01LN1306A”) and the project GLUES, the Stordalen Foundation (via the Planetary Boundary Research Network PB.net), the Earth League's EarthDoc program, and the Volkswagen Foundation via the project “Recurrent extreme events in spatially extended excitable systems: Mechanism of their generation and termination” (Grant No. 85391). The presented research has greatly benefited from discussions with Emilio Hernández-Garcia and Cristóbal López. Parts of the network calculations have been performed using the Python package pyunicorn56 (see http://tocsy.pik-potsdam.de/pyunicorn.php). pyunicorn is freely available for download at https://github.com/pik-copan/pyunicorn

PY - 2017

Y1 - 2017

N2 - 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 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.

AB - 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 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.

KW - physics.flu-dyn

KW - nlin.CD

KW - anisotropy

U2 - 10.1063/1.4971785

DO - 10.1063/1.4971785

M3 - Article

VL - 27

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 3

M1 - 035802

ER -