Abstract
We show that whenever there is a sharp drop in the numerical rank defined by a personalized PageRank vector, the location of the drop reveals a cut with small conductance. We then show that for any cut in the graph, and for many starting vertices within that cut, an approximate personalized PageRank vector will have a sharp drop sufficient to produce a cut with conductance nearly as small as the original cut. Using this technique, we produce a nearly linear time local partitioning algorithm whose analysis is simpler than previous algorithms.
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Andersen, R., Chung, F. (2007). Detecting Sharp Drops in PageRank and a Simplified Local Partitioning Algorithm. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_1
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DOI: https://doi.org/10.1007/978-3-540-72504-6_1
Publisher Name: Springer, Berlin, Heidelberg
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