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

0380325 - ÚI 2013 RIV US eng J - Journal Article
Hlinka, Jaroslav - Hartman, David - Paluš, Milan
Small-world topology of functional connectivity in randomly connected dynamical systems.
Chaos. Roč. 22, č. 3 (2012), art no 033107. ISSN 1054-1500. E-ISSN 1089-7682
R&D Projects: GA ČR GCP103/11/J068
Institutional support: RVO:67985807
Keywords : graph theory * nonlinear dynamical systems * small-world networks
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 2.188, year: 2012

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 are 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.
Permanent Link: http://hdl.handle.net/11104/0211061