The Bellman-Ford algorithm finds single source shortest paths by repeatedly relaxing distances until there are no more distances to relax. Relaxing distances is done by checking if an intermediate point provides a better path than the currently chosen path. After a number of iterations that is slightly less than the node count, we can check if the solution is optimal. If not, there is a cycle of negative edges that will provide better paths infinitely long.

This algorithm has the advantage over Dijkstra because it can handle graphs with negative edges, while Dijkstra is limited to non-negative ones. The only limitation it has are graphs with cycles that have an overall negative path, but this would just mean that there is no finite solution.