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We employ the recently developed theory of isospectral network reductions toanalyze multi-mode social networks. This procedure allows us to uncover thehierarchical structure of the networks we consider as well as the hierarchicalstructure of each mode of the network. Additionally, by performing a dynamicalanalysis of these networks we are able to analyze the evolution of theirstructure allowing us to find a number of other network features. We apply bothof these approaches to the Southern Women Data Set, one of the most studiedsocial networks and demonstrate that these techniques provide new information,which complements previous findings.

Uncovering Hierarchical Structure in Social Networks using Isospectral Reductions