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

Area of Science:

• Network science
• Complex systems analysis
• Graph theory applications

Background:

• Real-world complex systems are often analyzed using graph theory to understand their topological structure.
• The small-world property, characterized by short path lengths and high clustering, is a key network characteristic.
• Functional connectivity, quantifying statistical dependence between time series, is commonly used to infer network links.

Purpose of the Study:

• To investigate potential biases in small-world property estimation using functional connectivity measures.
• To determine if functional connectivity methods inflate small-world characteristics compared to random graph models.
• To assess the prevalence of these biases in coupled dynamical systems.

Main Methods:

• Analysis of functional connectivity measures, specifically correlation coefficients.
• Comparison of estimated network properties with established random graph models.
• Extensive parameter study using a multivariate linear autoregressive process.

Main Results:

• Functional connectivity measures, like correlation, exhibit partial transitivity, leading to upwardly biased small-world estimates.
• Small-world characteristics can be erroneously observed in connectivity graphs derived from randomly connected dynamical systems.
• The phenomenon's ubiquity and robustness were confirmed across various parameters.

Conclusions:

• The functional connectivity approach may inherently overestimate small-world network properties.
• Care must be taken when interpreting small-world characteristics derived from correlation-based functional connectivity.
• Findings have implications for understanding network topology in both linear and potentially nonlinear dynamical systems.