Axiomatic characterization of PageRank

This paper examines the fundamental problem of identifying the most important nodes in a network. To date, more than a hundred centrality measures have been proposed, each evaluating the position of a node in a network from a different perspective. Our work focuses on PageRank which is one of the most important centrality measures in computer science used in a wide range of scientific applications. To build a theoretical foundation for choosing (or rejecting) PageRank in a specific setting, we propose to use an axiomatic approach. Specifically, we propose six simple properties and prove that PageRank is the only centrality measure that satisfies all of them. In this way, we provide the first axiomatic characterization of PageRank in its general form.