Eigen Analysis of Networks

We present an overview of eigen analysis methods and their applications to network analysis. We consider several network analysis programs/procedures (Correspondence Analysis, NEGOPY, CONCOR, CONVAR, Bonacich centrality) that are at their core eigendecomposition methods. We discuss the various matrix representations of networks used by these procedures and we give particular attention to a variety of centering and normalizing procedures that are carried out prior to the analysis. We compare three types of iterative procedures with the standard SVD in terms of pragmatic concerns and the results produced by each method. We show how the initial matrix representations and the adjustments made between iterations influence the results obtained. Finally, we show that the eigen perspective clearly highlights the similarities and differences between different network analysis procedures.