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The authors propose a bipartite, distance-regular topology for interconnection networks to build large multiprocessor systems. The connectivity for these networks is the best possible and their average internodal distance is roughly equal to half the diameter. These features show that the proposed networks have relatively high densities, and are capable of maximal fault-tolerance. The topology allows efficient self-routing for both the nonfaulty and faulty network. For these networks the authors propose a semi-distributed fault-diagnosis algorithm which requires a relatively small computation overhead and generates considerably lower network traffic. The self-diagnostic scheme is in turn shown to be fault-tolerant. The most remarkable property of this topology is its symmetric partitioning capability, which is based on a combinatorial configuration known as the Hadamard matrix. On the basis of this partitioning property, the authors propose another semidistributed self-diagnosis algorithm which considerably improves the diagnosability of the partitioned network over the nonpartitioned network.