About Such Things as Unistors, Flow Graphs, Probability, Partial Factoring, and Matrices

The purpose here is to point out three things. 1) Topological circuit analysis, in which we look for trees, and topological flow-graph analysis, in which we look for loops, are intimately related, since both have to do with simultaneous linear algebraic equations. The intimate relationship becomes an indentity when we deal with Markoff probability diagrams, for which the circuit model of the problem and the flow-graph model of the problem are one and the same. 2) The expression for a flow-graph transmission in terms of the branch transmissions can often be made much more compact by a process called partial factoring. Fortunately, this process has a simple topological interpretation, so that the compact form is obtainable by inspection of the flow-graph. 3) Simultaneous linear matrix equations may be conveniently expressed in flow-graph form, whereupon the solution is obtainable by standard flow-graph reduction techniques.