# Common Graph Theory Problems and Algorithms #### Shortest path ![](Screen%20Shot%202021-04-05%20at%207.40.21%20AM.png) Algorithms: * BFS (unweighted graph), Dijkstra's, Bellman-Ford, Floyd-Warshall, A*, and many more #### Connectivity ![](Screen%20Shot%202021-04-05%20at%207.40.56%20AM.png) Algorithms: * Use union find data structure or any search algorithm (e.g. DFS) #### Negative Cycles ![](Screen%20Shot%202021-04-05%20at%207.43.12%20AM.png) Algorithms: * Bellman-Ford and Floyd-Warshall #### Strongly Connected Components ![](Screen%20Shot%202021-04-05%20at%207.45.31%20AM.png) Algorithms: * Tarjan's and Kosaraju's algorithm #### Traveling Salesman Problem ![](Screen%20Shot%202021-04-05%20at%207.46.43%20AM.png) Algorithms: * Held-Karp, branch and bound and many approximation algorithms #### Bridges ![](Screen%20Shot%202021-04-05%20at%207.48.20%20AM.png) #### Articulation Points ![](Screen%20Shot%202021-04-05%20at%207.48.47%20AM.png) #### Minimum Spanning Tree (MST) ![](Screen%20Shot%202021-04-05%20at%207.49.31%20AM.png) ![](Screen%20Shot%202021-04-05%20at%207.49.51%20AM.png) Algorithms: * Kruskal's * Prim's and Boruvka's algorithm #### Network Flow: Max Flow ![](Screen%20Shot%202021-04-05%20at%207.51.32%20AM.png) Algorithms: * Ford-fulkerson * Edmonds-Karp & Dinic's algorithm