Spectral Graph Theory Tools for Social Network Comparison

The problem faced in this paper is related to the comparison between two undirected networks on n actors. Actors are in two different configurations G k (k=1,2). Comparison is based on the evaluation of the how the relational node distances evolve in the passage from the first net (G 1) to the second net (G 2). The procedure consists of two steps: (i) define an appropriate relational distance among nodes of the two networks; (ii) compare the corresponding distance matrices. The first step is based on the so-called Euclidean Commute-Time Distance among the n nodes computed from a random walk on the graph and Laplacian matrix. The second step concerns the comparison between the obtained distance matrices by using Multidimensional Scaling techniques. The procedure has a wide range of application, especially for experimental purposes in social network applications where this issue has not been treated systematically.