An algorithm for the determination of longest distances in a graph

This paper presents an algorithm for ranking the vertices of a directed graph. Its space and time requirements are bounded byc ₁ n ² +c ₂, wheren is the number of vertices of the graph andc ₁,c ₂ are positive constants which are independent of the size or other properties of the graph.The algorithm can be easily modified to solve the problem of determining longest distances from a vertex to all other vertices in a positive real valued graph with at mostc ₁ n ² +c ₂ elementary operations; the same result holds for shortest distances in negative real valued graphs.