Graph algorithms are important in competitive programming because they allow programmers to solve problems that involve relationships, paths, and connectivity, which appear frequently in contests. Understanding graph concepts, such as nodes, edges, and adjacency, enables programmers to tackle problems related to networks, social connections, and map traversals. Key graph algorithms include BFS (Breadth-First Search), DFS (Depth-First Search), Dijkstra's for shortest paths, and Kruskal’s or Prim’s algorithms for minimum spanning trees. These algorithms help solve complex problems like shortest path finding, connectivity checks, and cycle detection. By mastering graph algorithms, competitive programmers can handle a wide range of challenges efficiently, making it a vital skill in contests where problem-solving speed and accuracy are essential.