  Edge centrality measures are functions that evaluate the importance of edges
in a network. They can be used to assess the role of a backlink for the
popularity of a website as well as the importance of a flight in virus
spreading. Various node centralities have been translated to apply for edges,
including Edge Betweenness, Eigenedge (edge version of Eigenvector centrality)
and Edge PageRank. With this paper, we initiate the discussion on the axiomatic
properties of edge centrality measures. We do it by proposing an axiomatic
characterization of Edge PageRank. Our characterization is the first
characterization of any edge centrality measure in the literature.

Social and Information Networks