Identifying centralized hubs within neural functional connections

The brain is a complex biological system with dynamic interactions between its sub-systems. One particular challenge in the study of this complex system is the identification of dynamic functional networks underlying observed neural activity. The interactions between different neural activity are quantified through measures of functional connectivity such as the phase synchrony measure. In previous studies, graph theoretical approaches have been implemented on the pairwise connectivity matrices to analyze these interactions and quantify them using clustering coefficient and path length. In this paper, we focus on finding specific nodes that demonstrate high degrees of centrality. The centrality measure helps pinpoint which nodes are important for maintaining an efficiently connected neural network. One challenge in applying graph theoretic measures to connectivity matrices is the lack of a unique relationship between the connectivity matrix and the corresponding binary graph. In this paper, we propose a new algorithm which finds the dasiaoptimalpsila binary graph based on different criteria including connectivity, clustering and the scale-free distribution of the network. The proposed framework is applied to an EEG study containing the error-related negativity (ERN) to identify hubs, a brain potential response that indexes endogenous action monitoring, to identify nodes with high centrality.