Since a path can run around the cycle many, many times and get any negative cost desired.in other words, a negative cycle invalidates the noton of distance based on edge weights.
In a networking or telecommunications mindset, this shortest path problem is sometimes called the min-delay path problem and usually tied with a widest path problem.
For example, the algorithm may seek the shortest (min-delay) widest path, or widest shortest (min-delay) path.
We have already seen how to solve this problem in the case where all the edges have the the relaxation criteria gives equalities.
Additionally, the path to any reachable vertex can be found by starting at the vertex and following the π's back to the source.
If one represents a nondeterministic abstract machine as a graph where vertices describe states and edges describe possible transitions, shortest path algorithms can be used to find an optimal sequence of choices to reach a certain goal state, or to establish lower bounds on the time needed to reach a given state.