Open Access
2008 Local Partitioning for Directed Graphs Using PageRank
Reid Andersen, Fan Chung, Kevin Lang
Internet Math. 5(1-2): 3-22 (2008).


A local partitioning algorithm finds a set with small conductance near a specified seed vertex. In this paper, we present a generalization of a local partitioning algorithm for undirected graphs to strongly connected directed graphs. In particular, we prove that by computing a personalized PageRank vector in a directed graph, starting from a single seed vertex within a set $S$ that has conductance at most $\alpha$, and by performing a sweep over that vector, we can obtain a set of vertices $S'$ with conductance $\Phi_{M}(S')= O(\sqrt{\alpha \log |S|})$. Here, the conductance function $\Phi_{M}$ is defined in terms of the stationary distribution of a random walk in the directed graph. In addition, we describe how this algorithm may be applied to the PageRank Markov chain of an arbitrary directed graph, which provides a way to partition directed graphs that are not strongly connected.


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Reid Andersen. Fan Chung. Kevin Lang. "Local Partitioning for Directed Graphs Using PageRank." Internet Math. 5 (1-2) 3 - 22, 2008.


Published: 2008
First available in Project Euclid: 25 November 2009

zbMATH: 1136.68317
MathSciNet: MR2504914

Rights: Copyright © 2008 A K Peters, Ltd.

Vol.5 • No. 1-2 • 2008
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