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

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.

The following article has been submitted to Chaos: An interdisciplinary journal of nonlinear science. After it is published, it will be found at http://chaos.aip.org/

References in corpus (4)

• Weight-conserving characterization of complex functional brain networks
• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• From brain to earth and climate systems: Small-world interaction networks or not?
• Small-world topology of functional connectivity in randomly connected dynamical systems

Cited by in corpus (14)

• Revealing networks from dynamics: an introduction
• Evolving networks in the human epileptic brain
• Analyzing complex functional brain networks: fusing statistics and network science to understand the brain
• FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
• Assortative mixing in functional brain networks during epileptic seizures
• Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity
• Quantifying information transfer and mediation along causal pathways in complex systems
• Beware of the Small-World neuroscientist!
• Inferring network properties from time series using transfer entropy and mutual information: validation of multivariate versus bivariate approaches
• Small-world topology of functional connectivity in randomly connected dynamical systems
• Ordinal methods for a characterization of evolving functional brain networks
• Generative Model Selection Using a Scalable and Size-Independent Complex Network Classifier
• Pairwise Network Information and Nonlinear Correlations
• A perturbation-based approach to identifying potentially superfluous network constituents