Testing Centrality in Random Graphs

Christian Tallberg

Centrality is an important concept in social network analysis which involves identification of important or prominent actors. Three common definitions of centrality are degree centrality, closeness centrality and betwenness centrality. These definitions yield actor indices which can be aggregated across actors to obtain a single group-level index. In this paper we consider how eight of these group-level indices can be used for graph centrality tests. Two of the tests are based on degree, whereas the remaining six tests are based on closeness. Our null hypothesis model, showing no centrality structure, is the Bernoulli graph model which we test against\ a block model reflecting graph centrality. We perform a simulation study where the power of the tests are compared.

Keywords: Bernoulli graphs; Closeness centrality; Degree centrality; Power of centrality tests; Random graphs; Stochastic blockmodels.

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