Small-world network architecture

Synchronization Likelihood (SL) is introduced recently to measure the interdependence within regions of brain. Suppose there are N channels in the brain, the SL for all pairwise combinations of channels is a square matrix of size N.

The first step to apply graph theoretical analysis to SL matrix is to convert the matrix into a binary graph. This is controlled by a threshold T. If the SL between a pair of channels i and j exceeds T, an edge is said to exist between i and j.

Once the synchronization matrix has been converted to a graph, the next step is to characterize the graph in terms of cluster coefficient C and path length L. The cluster coefficient is computed for all vertices of the graph and then averaged. It is a measure for the tendency of network elements to form local clusters. Path length L is the average shortest path connecting any 2 vertices of the graph.