Abstract
Topological analysis of the signal flow graph associated with the hybrid system of equations for a linear active or passive electrical network for which the element admittance matrix exists and is diagonal is considered. First, the term cancellation which occurs in Mason's topological formulas is investigated. Necessary and sufficient conditions on the signal flow graph topology such that a term in the expansion of the graph determinant and cofactors either cancels out with another term in the expansion or does not cancel are established. Properties of the associated network which result in non-cancelling terms are given and the number of non-cancelling terms is determined. Second, new signal flow graph topological formulas for the graph determinant and cofactors are proven. These formulas are such that no term cancellation occurs and are readily adaptable to computer implementation. In addition, the number of terms in these formulas is independent of the network tree used to formulate the signal flow graph. Examples are given to illustrate the new formulas.
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