A second limitation in previous EEG studies is the lack of mathematical characterization of the relationship of activity generated across the network of electrodes. Methods derived from the physics of complex systems (Boccaletti et al., 2006; Newman, 2006; Strogatz, 2001) allow structural or functional connections among brain regions to be represented as a comprehensive network (Bullmore and Sporns, 2009; Sporns et al., 2005). Graph theory has provided principled mathematical descriptions for the quantitative analysis of complex networks as described by Rubinov and Sporns (2010) and Kaiser (2011). For example, the studies investigating topological organization of the brain has revealed that the human brain network demonstrates small-world characteristics at the micro (neuron and synapse) and macro (region and pathway) scales on the brain (Bassett and Bullmore, 2006; Sporns and Zwi, 2004; Watts and Strogatz, 1998) — i.e. the network has a greater number of short intra-connections within local sub-networks and relatively fewer inter-connections between sub-networks. A variety of neurological and psychiatric diseases alter connectivity within brain networks (Catani and ffytche, 2005). Graph theory has been utilized to delineate functional and structural
