Local Graph Partitioning using PageRank Vectors

A local graph partitioning algorithm finds a cut near a specified starting vertex, with a running time that depends largely on the size of the small side of the cut, rather than the size of the input graph. In this paper, we present an algorithm for local graph partitioning using personalized PageRank vectors. We develop an improved algorithm for computing approximate PageRank vectors, and derive a mixing result for PageRank vectors similar to that for random walks. Using this mixing result, we derive an analogue of the Cheeger inequality for PageRank, which shows that a sweep over a single PageRank vector can find a cut with conductance φ, provided there exists a cut with conductance at most f(φ), where f(φ) is Ω(φ2 / log m), and where m is the number of edges in the graph. By extending this result to approximate PageRank vectors, we develop an algorithm for local graph partitioning that can be used to a find a cut with conductance at most φ, whose small side has volume at...

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Reid Andersen, Fan R. K. Chung, Kevin J. Lang
• Keywords: FOCS 2006, Graph Partitioning Algorithm, Local Graph Partitioning, PageRank Vectors, Theoretical Computer Science