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The push algorithm was proposed first by Jeh and Widom in the context ofpersonalized PageRank computations (albeit the name "push algorithm" wasactually used by Andersen, Chung and Lang in a subsequent paper). In this notewe describe the algorithm at a level of generality that make the computation ofthe spectral ranking of any nonnegative matrix possible. Actually, the maincontribution of this note is that the description is very simple (almosttrivial), and it requires only a few elementary linear-algebra computations.Along the way, we give new precise ways of estimating the convergence of thealgorithm, and describe some of the contribution of the existing literature,which again turn out to be immediate when recast in our framework.

The Push Algorithm for Spectral Ranking