Small-world topology of functional connectivity in randomly connected dynamical systems

TL;DR

This paper investigates how functional connectivity measures can bias the detection of small-world properties in complex systems, showing that even random systems may appear to have small-world topology due to methodological artifacts.

Contribution

It reveals that common functional connectivity measures can artificially induce small-world characteristics in connectivity graphs, challenging interpretations of such properties in empirical data.

Findings

Functional connectivity measures can bias small-world detection.

Randomly connected systems may appear to have small-world topology.

The phenomenon is robust across parameter variations in linear autoregressive models.

Abstract

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled dynamical systems, links among units of the system are commonly quantified by a measure of pairwise statistical dependence of observed time series (functional connectivity). We argue that the functional connectivity approach leads to upwardly biased estimates of small-world characteristics (with respect to commonly used random graph models) due to partial transitivity of the accepted functional connectivity measures such as the correlation coefficient. In particular, this may lead to observation of small-world characteristics in connectivity graphs estimated from generic randomly connected dynamical systems. The ubiquity and robustness of the phenomenon is documented by an extensive parameter study of its manifestation in a multivariate linear autoregressive process, with discussion of the potential relevance for nonlinear processes and measures.