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Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where k 2 machines jointly perform computations on graphs with n nodes (typically, n ≫ k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation., QC 20180905