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Topological methods of designing printed and integrated circuits have recently been the subject of much interest. A new algorithm is now presented for the construction of the graph of a circuit. Not only does this algorithm produce simpler graphs than it was possible to produce by the use of earlier methods, but it also retains much of the freedom normally associated with manual routing. Using this algorithm, conductors can be rerouted automatically if they lie in the path of another conductor, and certain options are left open as long as possible to minimise the probability of failure. There is no restriction on routing conductors among the terminals of a component. The experience gained with the algorithm so far is encouraging.