Prim's Algorithm for Minimum Spanning Tree

This document presents a universal MATLAB source program implementing Prim's algorithm for minimum spanning tree construction. The implementation employs adjacency matrix representation for graph data and features a priority queue mechanism for efficient edge selection. Key algorithmic components include vertex initialization, edge weight comparisons, and cycle prevention through visited node tracking. The program's modular design allows customization of input parameters including weighted graph data, starting vertex selection, and output formatting options. It handles various application scenarios such as data communication networks, infrastructure design, and routing optimization problems. The code implements Prim's algorithm through systematic steps: initializing with a random vertex, iteratively adding minimum-weight edges connecting visited and unvisited vertices, and maintaining the growing tree structure until all vertices are incorporated. The implementation includes error checking for invalid inputs and provides clear visualization options for the resulting spanning tree. This optimized MATLAB solution offers computational efficiency for large-scale graphs while maintaining educational clarity through commented code sections explaining each algorithm phase. Users can adapt the core functions for specific network topologies and weight metrics, saving significant development time in graph theory applications.