The Bellman-Ford algorithm is used by DVR protocols like RIP and
RIPv2.

Negative edge weights are found in various applications of graphs,
hence the usefulness of this algorithm.[2] If a graph contains a
"negative cycle", i.e., a cycle whose edges sum to a negative value,
then there is no cheapest path, because any path can be made cheaper
by one more walk through the negative cycle. In such a case, the
Bellmanâ€“Ford algorithm can detect negative cycles and report their
existence, but it cannot produce a correct "shortest path" answer if a
negative cycle is reachable from the source