Algorithms for ordering a sparse matrixAfor parallel triangular factorisation and for obtaining the parallel inverse ofAare given. The heuristic ordering method is based on graph manipulations. It attempts to minimise the completion time of parallel triangular factorisation while preserving the sparsity of the matrix. The inversion method proposed is based on the triangular factors ofA. The task of obtaining the ‘sparse inverse’ofAis represented by a directed acyclic graph. The algorithm and the graph for the full inversion ofAare also given. Claims are substantiated by experiments using test data from several electric networks.