A ranking system F is a functional that maps every finite strongly connected directed graph (SCDG) G=(V,E) into a reflexive, transitive, complete, and anti-symmetric binary relation ≤ on V
Node v has a self-edge (v,v) in G’, but does not in G. Otherwise G and G’ are identical. F satisfies SE iff for all u,w ≠ v:
(u ≤ v u <’ v) and (u ≤ w u ≤’ w)
PageRank satisfies SE: Suppose v has k outgoing edges in G. Let (r 1 ,…,r v ,…,r N ) be the rank vector of G, then (r 1 ,…,r v + 1/k ,…,r N ) is the rank vector of G’
‘ Representation theorems isolate the “essence” of particular ranking systems, and provide means for the evaluation (and potential comparison) of such systems ’ – Alon & Tennenholtz
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