*2.2.4 EEG FC using graph metric*

In the graph theory context EEG channels are taken as the graph nodes and connectivity values between them as edges. The usefulness of this metric has been reported to be of interest in brain neural network research to evidence changes in its topological structure. Two measures are used to define different types of neural network organization: one involves the nodal groups, the clustering coefficient (C) and the other the magnitude of the length of the path between nodes, length of the characteristic path L. For a given node, C measures the tendency to link from neighboring nodes, reflecting the extent of the local domain; while L is associated with the ability to integrate global information and, therefore, with the readiness for communication within the brain [110, 111]. Depending on the relative magnitudes of C and L, different levels of topological organization of a cortical brain network are defined. Thus, a network is considered "regular" when a high value of C and L is obtained from its graph representation, while a network is considered "random" when a low value of C and L is found. Between both types of network, the type called small world (SW) is defined when a graph has a high C magnitude and a low L magnitude. Consequently, SW neural networks are said to have a high level of local information distribution together with a high efficiency for global transfer information, both properties of great relevance for the dynamics of complex brain processing [110, 111]. For determining the SW level of a network NN, the C and L magnitudes are normalized with regard to the mean of a number (N = 100) of random networks having the same number of nodes, edges, and degree distributions as the network NN [112]. A network with approximately equal L and larger C than matched random networks (i.e., normalized L ~ 1 and normalized C > 1) is said to be a SW network. In the context of the musical perception, listening to Chinese

music (Guquin music excerpts versus silence and noise) in non-specialist subjects has been reported to produce an increase in functional connectivity (EEG phase coherence) in the alpha band, an improvement in cortical network organization of small world [73] and also a tendency to the random organization of the network as well -when a phase delay index is used that indicates a tendency to a more efficient but less economical architecture during musical listening [113]. Therefore, musical hearing somehow affects the topological structure of brain networks.
