This calculator helps you compute the Minimum Spanning Tree (MST) of an undirected graph using Prim's Algorithm. Suitable for students and professionals dealing with graph theory and network design.
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Data Source and Methodology
All calculations are rigorously based on the standard Prim's algorithm for calculating the Minimum Spanning Tree of a graph. Refer to "Introduction to Algorithms" by Cormen et al. for detailed methodology.
The Formula Explained
The Prim's algorithm works by starting with a single vertex and expanding the MST one edge at a time until all vertices are included. It uses a priority queue to efficiently select the minimum weight edge at each step.
Glossary of Terms
- Vertex: A node in the graph.
- Edge: A connection between two vertices, with an associated weight.
- MST: Minimum Spanning Tree, a subset of the edges that connects all vertices with the minimum total edge weight.
How It Works: A Step-by-Step Example
Consider a graph with 4 vertices and the following edges:
- 1, 2, 4
- 1, 3, 1
- 2, 3, 3
- 3, 4, 2
The MST found using Prim's algorithm would include edges with a total weight of 7, connecting all vertices with the minimal total weight.
Frequently Asked Questions (FAQ)
What is Prim's Algorithm?
Prim's Algorithm is a greedy algorithm that finds a Minimum Spanning Tree for a connected weighted graph.
Why use a Minimum Spanning Tree?
MSTs are useful in network design, such as designing the layout of a network with minimal cost.
What is the complexity of Prim's Algorithm?
The time complexity of Prim's algorithm is O(V^2), but can be reduced to O(E log V) using a priority queue.
Can Prim's Algorithm handle negative weights?
Yes, as long as the graph remains connected.
What data structure is used in Prim's Algorithm?
A priority queue is typically used to efficiently determine the next edge to add to the MST.
Formula (LaTeX) + variables + units
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- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
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