Recurrence networks—a novel paradigm for nonlinear time series analysis

TLDR

The paper introduces a novel method for analysing structural properties of complex‑system time series. It constructs a recurrence network by interpreting the recurrence matrix of a time series as a complex‑network adjacency matrix, linking temporally similar states. The approach outperforms existing techniques, unifies them as special cases, and shows that network topology reflects phase‑space density, providing new quantitative measures that complement traditional recurrence analysis.

Abstract

This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. It is demonstrated that there are fundamental relationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis.