On a Class of Directed Graphs—With an Application to Traffic-Flow Problems

Let G be a directed graph such that even edge e of G is associated with a positive integer, called the index of e. Then G is called a network graph if, at every vertex v of G, the sum of the indices of the edges terminating at v is equal to that of the edges incident from v. This paper obtains several theorems giving necessary and sufficient conditions for v directed graph to be a network graph, and applies the results to solving some problems of smoothing traffic flow.