Analytical relationships between metric and centrality measures of a network and its dual

The centrality and efficiency measures of a network G are strongly related to the respective measures on the dual G ⋆ and the bipartite B ( G ) associated networks. We show some relationships between the Bonacich centralities c ( G ) , c ( G ⋆ ) and c ( B ( G ) ) and between the efficiencies E ( G ) and E ( G ⋆ ) and we compute the behavior of these parameters in some examples.