The Theory of Nets

This paper presents the general concept of a weighted directed graph which we call a net. Illustrative examples leading up to the definition of a net indicate its applicability to a wide variety of problems in communication and network theory. A number of theorems concerning the proper paths of a net are established. A non-arithmetic matrix calculus is developed to facilitate computations and formalize proofs. In later papers, the techniques presented here will be exploited in the study of the theory of sequential machines.