Bellman-Ford Calculator
Find shortest paths with possible negative edge weights and detect negative-weight cycles. This educational calculator shows the result, explains the rule, and gives step-by-step reasoning.
Calculator
What this calculator teaches
Find shortest paths with possible negative edge weights and detect negative-weight cycles.
Graph theory and algorithm mathematics are core parts of discrete math and computer science. They help explain networks, dependency graphs, search, optimization, data structures, and route planning.
Formula & Symbols
| Concept | Formula or rule |
|---|---|
| Relaxation rounds | Repeat relaxation |V| - 1 times |
| Negative cycle test | One more improving relaxation means a negative cycle is reachable |
Worked Example
- Bellman-Ford can handle B>C:-2, unlike Dijkstra’s algorithm.
- Click Calculate to see the result and the algorithm steps.
- Change one edge, node, or weight and compare how the output changes.
When to use it
Common mistakes
Use arrows like A>B when direction matters. Use A-B when the edge should work both ways.
Weighted algorithms need entries such as A-B:5. If no weight is supplied, the calculator treats the edge weight as 1.
Some graph problems grow quickly. Hamiltonian path and similar searches are meant for small educational graphs.
FAQ
Related calculators
Use related discrete math and algorithm calculators to compare graph representations, paths, sets, and recurrence behavior.
Formula Explorer connections
Interpretation: This formula or algorithm measures graph structure, traversal, reachability, path cost or network connectivity. Assumption: Specify whether the graph is directed or weighted and whether negative edges, cycles or disconnected components are allowed by the chosen algorithm.