Network centralization with the Gil Schmidt power centrality index

Network centralization is a network index that measures the degree of dispersion of all node centrality scores in a network from the maximum centrality score obtained in the network. The Gil Schmidt power centrality index was developed for use in describing the political networks of Mexico, Gil and Schmidt [Gil, J., Schmidt, S., 1996a. The origin of the Mexican network of power. In: International Social Network Conference, Charleston, SC, USA, pp. 22–25; Gil, J., Schmidt, S., 1996b. The political network in Mexico. Social Networks 18, 355–381]. Upper bounds for network centralization, using the Gil Schmidt power centrality index, are derived for networks of fixed order and for when the network is bipartite, such as can arise from two mode data. In each case the networks that have maximum network centralization are described.