TL;DR
This paper introduces the first axiomatic characterization of Edge PageRank, a measure of edge importance in networks, and discusses its foundational properties.
Contribution
It provides the first axiomatic framework for edge centrality measures, specifically characterizing Edge PageRank.
Findings
Edge PageRank is uniquely characterized by certain axioms.
This work initiates the axiomatic study of edge centrality measures.
The characterization helps understand the fundamental properties of edge importance.
Abstract
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.
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