The Bellman-Ford algorithm solves the single-source shortest-paths problem in the general case in which edge weights may be negative. It returns a boolean value indicating whether there is a negative-weight cycle that is reachable from the source. If there is such a cycle, the algorithm indicates that no solution exists. If there is no such cycle, the algorithm produces the shortest paths and their weights.
Takes time.
Works like BFS


Use Graph Relax Method, call Relax on every edge n-1 times (n = number of vertex)

Find Negative Weight Cycle

It can also be used to find whether the graph has negative weight cycle.