How can I detect negative cycles in a graph?

What are negative cycles in a graph?

Negative cycles are cycles in a graph where the sum of the edge weights is negative, which can lead to infinite reductions in path costs.

How can I detect if a graph has a negative cycle?

You can use algorithms like the Bellman-Ford algorithm, which can detect negative cycles by checking for further relaxations after all edges have been processed.

Can you explain how the Bellman-Ford algorithm works?

Sure! The Bellman-Ford algorithm iteratively relaxes all edges and checks for negative cycles by seeing if any distance can still be reduced after V-1 iterations, where V is the number of vertices.

Are there any other methods to detect negative cycles?

Yes, another method is using the Floyd-Warshall algorithm, which can also find negative cycles while computing shortest paths between all pairs of vertices.