Speeding up the Floyd–Warshall algorithm for the cycled shortest path problem

On a network with a cycle, where at least one cycle exists, the Floyd–Warshall algorithm is one of the algorithms most used for determining the least cost path between every pair of nodes. In this work a new algorithm for this problem is developed that requires less computational effort than the Floyd–Warshall algorithm. Furthermore, we show that the basis of our algorithm is much easier to understand, which might be an advantage for educational purposes. A small example validates our algorithm and shows its implementation.