Abstract: The edges between nodes of a graph describe some sort of relationship between the two nodes. In this paper, we would like to efficiently determine the relationship between specific nodes of importance, which we call marked nodes, in a large graph. These relationships obtained must be optimal, which requires us to segregate the marked nodes from the less important nodes and group them together using partitioning algorithms. We introduce an improved algorithm which allows for the efficient addition of new marked nodes to a partition without rerunning the algorithm on previously marked nodes.
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