Graph algorithms play a crucial role in modeling and solving real-world problems across various fields such as economics, biology, and network routing. This text delves into 20 widely used graph algorithms, including Breadth-First Search (BFS), Depth-First Search (DFS), Dijkstra's, A* algorithm, and more, explaining their structures and applications. BFS is leveraged in peer-to-peer networks and web crawlers, while DFS is used in scheduling and network analysis. Dijkstra's and the A* algorithms find shortest paths in network routing. The Minimum Spanning Tree algorithm optimizes network design, and Maximum Flow aids in network and operations research. Algorithms like Tarjan's and Kosaraju's identify strongly connected components in graphs, while others like Floyd-Warshall and Kruskal's help in shortest path and minimum spanning tree calculations. These algorithms are integral in computer science, artificial intelligence, operations research, and network design, offering solutions to complex problems by efficiently managing data represented as graphs.