A weighted small world network measure for assessing functional connectivity

There is a growing need to develop measures that can characterize complex patterns of functional connectivity among brain regions. Graph theoretic measures have emerged as an important way to characterize the multivariate connectivity between nodes in a network, which have been successfully applied to neurophysiologic activity. In this paper, we propose a new small-world measure based on advances in both the bivariate measures underlying the graph theoretic approach, as well as in the definition of the measure for weighted graphs. Specifically, we recently proposed a new bivariate time-frequency phase-synchrony (TFPS) measure, which quantifies the dynamic nature of the interactions between neuronal oscillations with a higher time-frequency resolution than previous approaches and is better at isolating relevant activity. The proposed graph theoretic measures, weighted clustering coefficient and path length, represent a new approach to the calculation of weighted graph measures based on this improved bivariate TFPS measure. The new graph theoretic measures are applied to two datasets. The first is a well-known social network, Zachary's Karate Club. The second application contains event-related potential (ERP) indexing the well-known error-related negativity (ERN) component related to cognitive control. Results indicate that the new measures outperform the previously published weighted graph measures, and produces expectable results for both applications.