Flow graphs, signal flow graphs, and graph determinants

The flow graph, introduced by C. L. Coates, is a structure, allied to the signal flow graph, which allows the solution of a system of linear equations to be found in a way which avoids certain redundancies. It is shown in the paper how the essential advantages of Coates´s theory can be incorporated into signal-flow-graph analysis. Where network theory is concerned it seems preferable to retain the signal-flow-graph form, and the reasons for this are discussed. In addition, the precise relations between graph determinants and the determinants of ordinary algebraic theory are examined. The paper concludes with a comparison of the algebra of flow-graph and of signal-flow-graph transformations.