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.

Statistical analysis consisted of independent samples t-tests and linear regression of the plots of C and L as a function of threshold T. In order to investigate correlations between changes in topological parameters with cognitive measures, the authors calculated Pearson's correlation coefficient between MMSE(a measure of cognitive function) scores and both cluster coefficient and path length.