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.

doi:10.1063/1.4971785

Cited by 11 publications

(19 citation statements)

References 61 publications

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“…One recent example of such a measure is the edge anisotropy, which takes the spatial directionality of edges adjacent to a given node into account. It has been shown that edge anisotropy supplements traditional topological measures like degree or betweenness by indicating the orientation of flows underlying networks constructed from spatio-temporal data [17].…”

Section: Introductionmentioning

confidence: 99%

Edge directionality properties in complex spherical networks

2019

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Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation and trade networks. In climate networks, our approach highlights relevant patterns like large-scale circulation cells, the El Niño-Southern Oscillation and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.

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Section: Introductionmentioning

confidence: 99%

Edge directionality properties in complex spherical networks

2019

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“…The contact with network theory 24 is made when the matrix representing the transfer operator is interpreted as the adjacency matrix of a network [1][2][3][4]17,22,23 , so that the weight of a link between two nodes is given by the amount of flow between the corresponding spatial locations. An alternative viewpoint in characterizing fluid flows with network techniques assigns links between spatial regions according to statistical correlations between their dynamical variables, leading to correlation-based flow networks [25][26][27] and making a connection with the broad field of climate networks [28][29][30][31] .…”

Section: Introductionmentioning

confidence: 99%

Clustering coefficient and periodic orbits in flow networks

Ser‐Giacomi

Hernández-Garcı́a

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e. graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of τ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of τ reveals the presence of periodic orbits of period 3τ which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea.The Lagrangian description of fluid dynamics, which focuses on the motion of the fluid particles as they are advected by the flow, provides a useful bridge between the theory of dynamical systems and the analysis of fluid transport and mixing, so that techniques and results can be transferred from one field to the other. Modern network theory has also been brought into contact with fluid dynamics and dynamical systems through the concept of flow networks, in which the motion of fluid particles between different regions is represented by links in a graph. In this paper we use the flow network framework to show that the clustering coefficient, a standard measure in network theory, identifies periodic orbits, fundamental objects in the theory of dynamical systems and also of importance in the context of fluid motion.

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“…Molkenthin et al 62 analyze networks constructed from correlations among variables undergoing advection-diffusion-reaction dynamics. The network perspective is used to demonstrate that the local anisotropy (a member of a new class of spatial network characteristics) of edges incident to a given vertex provides useful information about the local geometry of the flow represented by the network.…”

Section: Correlation-based Flow Networkmentioning

confidence: 99%

Introduction to Focus Issue: Complex network perspectives on flow systems

Donner

Hernández-Garcı́a

Ser‐Giacomi

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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During the last few years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of dynamical systems from a variety of different fields. Among others, recent successful examples include (i) functional (correlation) network approaches to infer hidden statistical interrelationships between macroscopic regions of the human brain or the Earth's climate system, (ii) Lagrangian flow networks allowing to trace dynamically relevant fluid-flow structures in atmosphere, ocean or, more general, the phase space of complex systems, and (iii) time series networks unveiling fundamental organization principles of dynamical systems. In this spirit, complex network approaches have proven useful for data-driven learning of dynamical processes (like those acting within and between sub-components of the Earth's climate system) that are hidden to other analysis techniques. This Focus Issue presents a collection of contributions addressing the description of flows and associated transport processes from the network point of view and its relationship to other approaches which deal with fluid transport and mixing and/or use complex network techniques.

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Edge anisotropy and the geometric perspective on flow networks

Cited by 11 publications

References 61 publications

Edge directionality properties in complex spherical networks

Edge directionality properties in complex spherical networks

Clustering coefficient and periodic orbits in flow networks

Introduction to Focus Issue: Complex network perspectives on flow systems

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