Dominating Centrality Set: A New Measure on the Network Coverage of Influential Center Nodes

There is a list of traditional measures on the centrality of a network, but they may provide misleading suggestions when there are more than one center in a network. Even a sequential selection on the centers are performed, the revelation of a truly influential set of the center nodes is difficult to achieve due to the curse of double counting. In this work, we introduce a new measure on the network coverage of the influential set of center nodes via a new graph-theoretic tool called the dominating centrality set (DCS). To calculate the DCS efficiently, we derive the exact formulas for counting the number of cycles that contains a specific node. We demonstrate this method to the analysis of Amazon product network and the Web of Science citation network.