Axiomatic Characterization of Distance-based Centralities

I will present our initial results concerning the characterization of the distance-based centralities. First, we characterize distance based centralities using Sabidussi's operations of adding and moving edges. Then, by adding one axiom we obtain a natural class of additive distance-based centralities. An additive distance-based centrality is defined by a vector a = <a_1,a_2,...,a_k...>, where a_k is the gain from node at distance k. We analyze the conditions on this vector imposed by axioms from the literature and characterize the Degree Centrality, the k-Degree Centrality, and the Size-of-the-component Centrality using new axioms of k-Fairness and k-Gain-loss.