The paper reviews the application of diakoptics and graph theory in the analysis of compressible flow in complex pipe network systems. A new method for partitioning the network based on alternative methods of cutting branches leads to an extension of the diakoptics theory which results, in practical terms, in a more computationally efficient solution for the simulation of pipe flows. An algorithm for re-referencing nodes and branches results in regular sparse matrices that are easily obtained from a branch-node connection list. The resulting matrices contain only non-zero elements. The computational advantages of the new cut method have been demonstrated by comparing them to other cut methods when applied to a range of pipe network simulation examples.