Enter Graph Data
Example Data Table
Use this sample graph to test the calculator quickly.
| Edge | Weight | Notes |
|---|---|---|
| A - B | 4 | Main connection |
| A - C | 2 | Low cost path |
| B - C | 1 | Cheapest local edge |
| B - D | 5 | Direct route |
| D - E | 2 | Efficient final link |
Formula Used
A minimum spanning tree minimizes the sum of selected edge weights while connecting all vertices without cycles.
Objective: Minimize Total Weight = Σ w(e) Subject to: 1. All vertices are connected. 2. No cycle is formed. 3. Selected edges = |V| - 1 for a connected graph. Savings = Sum of all input edge weights - MST total weight
Kruskal sorts edges and accepts the lightest non-cycling edges. Prim grows one connected tree by repeatedly adding the cheapest outward edge.
How to Use This Calculator
- Enter node labels if you want explicit vertex control.
- Paste one weighted edge per line using Node1,Node2,Weight.
- Select Kruskal or Prim.
- Enter a start node when using Prim.
- Click the calculate button.
- Review selected edges, total cost, connectivity status, and decision steps.
- Use CSV or PDF export for reports, coursework, or planning notes.
Frequently Asked Questions
1. What does this calculator find?
It finds the lowest total set of edges that connects all graph nodes without creating cycles. If the graph is disconnected, it returns the lightest reachable forest.
2. When should I use Kruskal?
Use Kruskal when you want an edge-sorting approach. It works well for sparse graphs and clearly shows which edges were accepted or rejected.
3. When should I use Prim?
Use Prim when you prefer growing the tree from one start node. It is intuitive for network expansion and local connection planning.
4. Does the starting node change the total result?
For many connected graphs, different start nodes still produce the same minimum total. If multiple valid trees exist, the edge set may differ.
5. Can weights be decimals or negative values?
Yes. The calculator accepts numeric weights, including decimals and negative values. The algorithm still minimizes the overall selected total correctly.
6. Why are some edges rejected?
Rejected edges would create a cycle or fail to improve the current minimum structure. The decision table explains each acceptance or rejection step.
7. What does weight reduction mean?
It compares the sum of all entered edge weights with the final tree weight. This helps show the efficiency gained by removing unnecessary links.