Spectral Embedding Procedure for Social Network Comparison

A key issue in social network analysis is related to the comparison between several observed networks on n actors. To this end, a special graph embedding procedure derived from the spectral properties of the networks is proposed. The procedure consists of two steps: i) define an appropriate metric among the observed networks based on the properties of the eigenvalues/eigenvectors of the so-called Laplacian matrix; ii) compare the corresponding distance matrices among the n actors within each network. The purpose is twofold: on the one hand we aim to define a matrix of actor distances and consequently to use the actors embedding for network comparison; on the other hand, we will be also able to measure the distances among the global network structures, considering them as points in a multivariate space. We will show applications in both exploratory social network analysis and network statistical modelling.