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Network solution by tearing consists of partitioning the network into subnetworks, solving each subnetwork separately, and then combining the subnetwork solutions to obtain the solution of the entire network. In this paper it is shown that all recently proposed sparse matrix algorithms for network solution by tearing belong to a set of algorithms which is derived by applying block matrix elimination to a partitioned system of network equations. The computational requirements of the algorithms are determined and compared. Equation sparsity is considered at all levels in the solution process. In particular, the structures of the equations at the subnetwork level as well as the interconnection level are analyzed in detail.