Abstract
Algorithms that exploit the duality between maximum concurrent flow and sparse cuts in a graph can effectively discover hierarchical community structures in social networks. We analyze the maximum concurrent flow on random bipartite graphs and compare the results to two bounds based on graph structure.. The minimum degree bound is based on a sparse cut that removes a node of minimum degree. The other is the “gridlock” bound, where all edges are saturated with flow. We show that the gridlock bound is more constraining when the minimum degree of the graph is sufficiently large, and provide a way to calculate this bound on graphs of diameter three, which occurs with high probability on larger random bipartite graphs.
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