Graph Theory Models and Methods

In the fields of computer algorithms and mathematical modeling, graph theory represents a critically important domain. It encompasses numerous classical algorithms and methodologies such as shortest path algorithms (implemented using Dijkstra's or Floyd-Warshall approaches), matching problems (including bipartite matching solutions), postman route optimization and traveling salesman problems (featuring heuristic and exact solution methods), minimum spanning tree algorithms (Prim's and Kruskal's implementations), and network flow optimization (Ford-Fulkerson and Edmonds-Karp algorithms). These algorithmic techniques find practical applications across diverse real-world scenarios including network routing protocols, engineering optimization challenges, and social network analysis. The material provides comprehensive MATLAB code implementations that demonstrate key graph theory functions like graph representation using adjacency matrices, pathfinding algorithms with proper distance tracking, and optimization solvers with clear variable naming conventions. Each program includes detailed comments explaining the algorithmic workflow and data structure usage, enabling readers to effectively understand and implement graph theory concepts through hands-on experimentation.