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Edge anisotropy and the geometric perspective on flow networks
Nora Molkenthin1, Hannes Kutza1, Liubov Tupikina1
1Research Domain IV - Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany.
Chaos (Woodbury, N.Y.)
|April 3, 2017
Summary
This study introduces geometric analysis for spatial networks, using edge anisotropy to reveal geophysical flow structures. Combining geometric and topological views enhances understanding of complex systems from observational data.
Area of Science:
- Network Science
- Geophysics
- Geometric Analysis
Background:
- Spatial networks are crucial across disciplines.
- Traditional analysis often overlooks spatial constraints, focusing solely on topology.
- A geometric perspective is needed to capture spatial distribution and alignment.
Purpose of the Study:
- To introduce a geometric viewpoint for analyzing spatial networks.
- To define and quantify edge anisotropy for characterizing connection directedness.
- To demonstrate the utility of geometric measures in understanding geophysical flows.
Main Methods:
- Defining edge anisotropy as a measure of spatial directedness.
- Analyzing local anisotropy of edges connected to a vertex.
- Constructing networks from spatio-temporal data for geophysical flow analysis.
Main Results:
- Local edge anisotropy provides insights into the geometry of geophysical flows.
- Geometric properties complement traditional topological network characteristics.
- Integrated structural and geometric analysis aids in identifying flow structures.
Conclusions:
- A geometric perspective, particularly edge anisotropy, offers valuable insights into spatial networks.
- Combining topological and geometric network analysis enhances the understanding of complex systems.
- This approach aids in deciphering underlying flow structures from scalar observations.