Ambiguities in recurrence-based complex network representations of time series

TL;DR

This paper critically examines the use of recurrence-based complex networks for analyzing time series, highlighting potential ambiguities and proposing rigorous interpretations of network measures in terms of invariant phase-space properties.

Contribution

It identifies limitations and artifacts in recurrence-based network representations and offers a systematic framework for their proper interpretation in dynamical systems analysis.

Findings

Artifacts can arise when interpreting network topology without considering phase-space invariants

A systematic study of the limitations of recurrence networks in representing dynamical properties

Proposes rigorous interpretations of clustering coefficient and betweenness centrality in terms of invariant objects

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.