Social Networks Comparison by Using Laplacian Matrix and Euclidean Commute Time Distance

The presented paper deals with the comparison between two social networks with the same set V of actors. The main purpose is to develop an exploratory strategy to investigate the relational differences (or similarities) between networks. Markov Chain on graph is used in order to introduce a special euclidean node-distance function. This distance is computed by means of the laplacian matrix L. The procedure generates for each of the two networks a distance matrix Δk (k = 1,2). differences are detected by projecting these matrices in a common and more parsimonious Euclidean space obtained by a multidimensional scaling and a procrustes analysis.