Abstract :
This paper presents in one listing those properties of the path matrix of a graph which are fundamental and interesting in nature. Included are 1) a relation between the path matrix and the incidence matrix, 2) the rank of the path matrix, 3) relations between paths and cut sets, and 4) relations between paths and circuits (Ashenhurst´s lemmas). Also included are a number of necessary conditions for the realizability of a matrix as a path matrix of a graph.
