Bringing order to network centrality measures

We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative restatement of many conjectures that were previously cumbersome to formalize. Moreover, it produces an approximation scheme useful for network scientists. We explore some of these uses and formulate new conjectures that are of independent interest.