Ambiguities in recurrence-based complex network representations of time series

Abstract

Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.

References in corpus (10)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Recurrence Plots for the Analysis of Complex Systems
• Synchronization in complex networks
• From time series to complex networks: the visibility graph
• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• Complex Network Approach for Recurrence Analysis of Time Series
• Random Geometric Graphs
• The backbone of the climate network
• Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity

Cited by in corpus (35)

• Complex network approaches to nonlinear time series analysis
• Recurrence networks - A novel paradigm for nonlinear time series analysis
• Recurrence-based time series analysis by means of complex network methods
• How to avoid potential pitfalls in recurrence plot based data analysis
• Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks
• The Geometry of Chaotic Dynamics -- A Complex Network Perspective
• Analytical framework for recurrence-network analysis of time series
• Geometric detection of coupling directions by means of inter-system recurrence networks
• Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices
• From the time series to the complex networks: the parametric (dynamical) natural visibility graph
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
• Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes
• Multiscale characterization of recurrence-based phase space networks constructed from time series
• Uniform framework for the recurrence-network analysis of chaotic time series
• Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions
• Fractal and complex network analyses of protein molecular dynamics
• Phase space reconstruction for non-uniformly sampled noisy time series
• Geometric signature of complex synchronisation scenarios
• Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions
• Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows
• Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls
• Disentangling regular and chaotic motion in the standard map using complex network analysis of recurrences in phase space
• Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
• Network Measures of Mixing
• Lagrangian coherent sets in turbulent Rayleigh-Bénard convection
• Experimental observation of a chaos-to-chaos transition in laser droplet generation
• Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection
• Distinguishing Cell Phenotype Using Cell Epigenotype
• Multiplex Recurrence Networks from multi-lead ECG data
• Recurrence network analysis in a model tripartite quantum system
• A bibliographic view on recurrence plots and recurrence quantification analyses
• Finding metastable states in real-world time series with recurrence networks
• RQA Application for the Monitoring of Financial and Commodity markets state
• Exploration of period-doubling cascade route to chaos with complex network based time series construction