Beyond good partition shapes: an analysis of diffusive graph partitioning. ... We then regard Bubble-FOS/C, which has been shown in previous experiments to produce solutions with good partition shapes and other favorable properties. In this paper we prove that it computes a relaxed solution to an edge cut minimizing binary quadratic program (BQP). This result provides the first substantial theoretical insight why Bubble-FOS/C yields good experimental results in terms of graph partitioning metrics. Moreover, we show that in bisections computed by Bubble-FOS/C, at least one of the two parts is connected. Using the aforementioned relation between FOS/C and random walks, we prove that in vertex-transitive graphs both parts must be connected components.

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