text: The method is based on the generated loops and the equations are simply mathematical representation of Kirchhoff's second law which states that the sum of the pressure-drops around any loop should be zero. Before using loops method the fundamental set of loops need to be found. Basically the fundamental set of loops can be found by constructing spanning tree for the network. The standard methods for producing spanning tree is based on a breadth-first search or on a depth-first search which are not so efficient for large networks, because the computing time of these methods is proportional to n, where n is the number of pipes in the network. More efficient method for large networks is the forest method and its computational time is proportional to n*logn.
  The loops that are produced from the spanning tree are not the best set that could be produced. There is often significant overlap between loops with some pipes shared between several loops. This usually slows convergence, therefore the loops' reduction algorithm needs to be applied to minimize the loops overlapping. This is usually performed by replacing the loops in the original fundamental set by smaller loops produced by linear combination of the original set.