A Collection of Classic Graph Theory Algorithms

Graph theory algorithms serve as essential computational tools for processing network-structured data in computer science, with extensive applications in path planning, social network analysis, and related domains. This MATLAB-based algorithm collection provides learners with complete practical solutions, enabling rapid theoretical validation without reinventing fundamental implementations. The core algorithms in this collection primarily address three classical problem categories: - Shortest-path algorithms (e.g., Dijkstra and Floyd-Warshall) solve optimal route problems between two nodes, particularly suitable for transportation navigation system modeling - Minimum spanning tree algorithms (e.g., Prim's and Kruskal's) address cost optimization scenarios like network cabling - Network flow algorithms (e.g., Ford-Fulkerson) analyze maximum capacity in pipeline transport and data packet transmission systems MATLAB's matrix operation capabilities are particularly well-suited for handling graph representations through adjacency matrices, while its visualization features enable intuitive demonstration of algorithmic steps. For instance, in Dijkstra's algorithm implementation, developers can directly observe how relaxation operations progressively update node distance values through iterative matrix manipulations. For educational applications, these ready-to-use implementations allow students to modify parameters (such as edge weights and node counts) and observe corresponding algorithmic behavior changes. This hands-on approach facilitates deeper understanding of greedy strategies and dynamic programming concepts in graph theory compared to pure theoretical study. Note that practical applications require adjustments to data structures and termination conditions based on specific scenarios - for example, sparse graphs are more efficiently handled using adjacency list storage instead of matrix representations.