A Local Graph Partitioning Algorithm Using Heat Kernel Pagerank

Abstract

We give an improved local partitioning algorithm using heat kernel pagerank, a modified version of PageRank. For a subset $S$ with Cheeger ratio (or conductance) $h$, we show that at least a quarter of the vertices in $S$ can serve as seeds for heat kernel pagerank that lead to local cuts with Cheeger ratio at most $O(\sqrt{h})$, improving the previous bound by a factor of $\sqrt{\log s}$, where s denotes the volume of $S$.