Measuring network centrality using hypergraphs

Networks abstracted as graph lose some information related to the super-dyadic relation among the nodes. We find natural occurrence of hyperedges in co-authorship, co-citation, social networks, e-mail networks, weblog networks etc. Treating these networks as hypergraph preserves the super-dyadic relations. But the primal graph or Gaifmann graph associated with hypergraphs converts each hyperedge to a clique losing again the n-ary relationship among nodes. We aim to measure Shapley Value based centrality on these networks without losing the super-dyadic information. For this purpose, we use co-operative games on single graph representation of a hypergraph such that Shapley value can be computed efficiently[1]. We propose several methods to generate simpler graphs from hypergraphs and study the efficacy of the centrality scores computed on these constructions.