Minimum Spanning Tree (Kruskal's Algorithm) Calculator

This calculator helps you find the Minimum Spanning Tree (MST) of a graph using Kruskal's Algorithm. Ideal for students and professionals in graph theory, it solves the problem of connecting all vertices with the minimum total edge weight.

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Data Source and Methodology

This tool relies on the standard Kruskal's Algorithm for computing the Minimum Spanning Tree. For more details, refer to authoritative sources such as textbooks on graph theory.

The Formula Explained

Using Kruskal's Algorithm, the graph's edges are sorted by weight, and the smallest edges are added to the MST until all nodes are connected without forming a cycle.

Glossary of Terms

How It Works: A Step-by-Step Example

Consider a graph with nodes 1, 2, and 3, and edges (1,2,3), (2,3,4). Enter this data, and the calculator will find the MST by first sorting edges by weight, then using a union-find structure to ensure no cycles, and finally outputting the MST.

Frequently Asked Questions (FAQ)

What is Kruskal's Algorithm?

Kruskal's Algorithm is a greedy algorithm used to find the MST of a graph by sorting edges and adding them to the MST in order of increasing weight.

Can this calculator handle directed graphs?

No, Kruskal's Algorithm is only applicable to undirected graphs.

What is a Minimum Spanning Tree?

A MST is a subset of edges connecting all nodes in a graph with the minimum possible total edge weight.

How are cycles avoided in Kruskal's Algorithm?

Cycles are avoided using a union-find data structure that tracks node connectivity.

Why use Kruskal's Algorithm?

It's efficient for sparse graphs and helps understand fundamental graph theory concepts.

Tool developed by Ugo Candido.
Content reviewed by the AlgorithmCalculator Expert Team.
Last reviewed for accuracy on: October 15, 2023.

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