MATLAB Source File for Dijkstra's Algorithm with Shortest Path Implementation

In this article, I present a comprehensive MATLAB source file implementation of Dijkstra's algorithm with detailed explanations. Dijkstra's algorithm is a classical method for solving shortest path problems in weighted graphs, widely applied in computer science and operations research. The algorithm operates by systematically expanding from the starting node to explore other nodes in the graph, progressively identifying the shortest paths. The MATLAB implementation employs key programming structures including priority queue management using min-heap operations, distance matrix initialization, and predecessor tracking for path reconstruction. The source file outputs both the shortest distance values and the complete path sequences, demonstrating the algorithm's efficiency and practical utility. The implementation features adjacency matrix representation for graph storage and utilizes vectorized operations for optimal performance. Additionally, we analyze the algorithm's time complexity of O(V²) for dense graphs (where V represents vertices) and space complexity of O(V) for storage requirements, providing insights into computational efficiency and scalability. Through careful code structuring with functions for node selection, distance updates, and path backtracking, this MATLAB resource serves as a valuable tool for both academic research and industrial applications in network optimization and route planning.