What are negative weight cycles in graphs?

Can you explain what negative weight cycles are in graph theory?

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

Why are negative weight cycles important in algorithms?

They are crucial because they can affect algorithms like Bellman-Ford, which detects them to prevent incorrect shortest path calculations.

How can I detect negative weight cycles in a graph?

You can use the Bellman-Ford algorithm, which iterates through the edges and checks for further reductions in path costs.

What happens if a graph has a negative weight cycle?

If a graph has a negative weight cycle, the shortest path to some vertices may not be well-defined, as you can keep reducing the path cost indefinitely.