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The problem of connectivity is an extremely important one in the context of massive graphs. In many large communication networks, social networks and other graphs, it is desirable to determine the minimum-cut between any pair of nodes. The problem is well solved in the classical literature, since it is related to the maximum-flow problem, which is efficiently solvable. However, large graphs may often be disk resident and such graphs cannot be efficiently processed for connectivity queries. This is because the minimum-cut problem is typically solved with the use of a variety of combinatorial and flow-based techniques which require random access to the underlying edges in the graph.
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