Can recurrence networks show small world property?

TL;DR

This paper investigates how the properties of recurrence networks derived from chaotic time series change with increasing threshold, revealing a transition from non-small-world to small-world and eventually to random graph structures.

Contribution

It provides the first systematic analysis of recurrence network properties at large thresholds, showing the conditions under which small-world characteristics emerge.

Findings

Recurrence networks at typical thresholds do not exhibit small-world properties.

Increasing the threshold can induce a small-world topology in recurrence networks.

At very high thresholds, the network resembles a classical random graph.

Abstract

Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold of the network are quite well understood, what happens as the threshold increases beyond the usual operational window is still not clear from a complex network perspective. The present Letter is focused mainly on the network properties at intermediate-to-large values of the recurrence threshold, for which no systematic study has been performed so far. We argue, with numerical support, that recurrence networks constructed from chaotic attractors with \epsilon equal to the usual recurrence threshold or slightly above cannot, in general, show small-world property. However, if the threshold is further increased, the recurrence network topology initially changes to a small-worldstructure and finally to that of a classical random graph as the threshold approaches the size of the strange attractor.