Positional Dominance: Concepts and Algorithms

Centrality indices assign values to the vertices of a graph such that vertices with higher values are considered more central. Triggered by a recent result on the preservation of the vicinal preorder in rankings obtained from common centrality indices, we review and extend notions of domination among vertices. These may serve as building blocks for new concepts of centrality that extend more directly, and more coherently, to more general types of data such as multilayer networks. We also give efficient algorithms to construct the associated partial rankings.