MST Kruskal Algorithm Calculator

Example Data Table

Formula Used

Kruskal algorithm builds a minimum spanning tree by sorting all edges in nondecreasing weight order.

MST condition: choose edge e = (u, v) only when Find(u) is not equal to Find(v).

Total weight: MST Weight = sum of all selected edge weights.

Connected graph rule: a valid spanning tree has V - 1 selected edges, where V is the number of vertices.

Cycle rule: if both endpoints already belong to the same component, the edge creates a cycle and is rejected.

How To Use This Calculator

1. Enter one weighted edge per line.
2. Use comma format, such as A,B,7.
3. You may also use space format, such as A B 7.
4. Add isolated vertices in the optional vertex field.
5. Select how duplicate edges should be handled.
6. Choose decimal places for the displayed total.
7. Press the calculate button.
8. Review selected edges, rejected edges, and total cost.
9. Download the result as CSV or PDF.

About the MST Kruskal Algorithm Calculator

This calculator helps students study minimum spanning trees. It accepts a weighted, undirected graph. Each line represents one edge. The tool sorts edges by weight. It then selects safe edges one by one. A safe edge connects two different components. That rule prevents cycles. The final tree links all reachable vertices with minimum total cost. It also supports repeat practice without changing page files.

Why Kruskal Method Matters

Kruskal method is simple and powerful. It works well when edge lists are easier to manage than adjacency tables. Many network problems use the same idea. Road planning, cable layout, circuit design, and clustering can all use minimum spanning trees. The algorithm does not need a starting vertex. It studies the whole edge set first.

What This Tool Shows

The result area shows sorted edges, selected edges, rejected edges, total weight, vertex count, edge count, and component count. Rejected edges are important. They show where a cycle would appear. This makes the calculator useful for homework checking and classroom demonstrations. The example table gives ready input for practice.

How The Calculation Works

The calculator uses a disjoint set structure. This structure is also called union find. Each vertex starts in its own set. The find operation checks the current root of a vertex. The union operation joins two different sets. Path compression and rank rules make these operations fast. After sorting, every edge is tested. If both endpoints already share one root, the edge is rejected. Otherwise, it is accepted.

Interpreting The Result

A connected graph with V vertices should have V minus one selected edges. If fewer edges are selected, the graph is disconnected. In that case, the result is a minimum spanning forest. The total weight still describes the best available connection inside each component. Always review vertex names and edge weights before trusting a final answer.

Good Input Practice

Use one edge per line. Separate values with commas or spaces. Valid lines include A,B,4 and A B 4. Negative weights are accepted. Loops are ignored because they cannot improve a spanning tree. Duplicate edges can be filtered or kept based on your option. Clean input gives clearer steps and better exports.

FAQs