Graph theory is a fundamental area in competitive programming, and a wide range of problems are based on graph traversal, shortest paths, and connectivity. The key to mastering graph problems is recognizing the underlying structure of the problem, such as whether it's directed or undirected, weighted or unweighted, and whether it involves cycles. Some of the most common algorithms used in graph problems include Breadth-First Search (BFS) for unweighted shortest paths, Depth-First Search (DFS) for exploring all possible paths, and Dijkstra's algorithm for finding the shortest path in weighted graphs. For negative weights, Bellman-Ford or Floyd-Warshall algorithms are more appropriate. Graph problems often appear in variations like minimum spanning trees (MST), where algorithms like Kruskal's or Prim's are used, or in problems related to bipartite graphs, where matching algorithms like the Hungarian algorithm may be applied. When approaching a graph problem, start by drawing a rough sketch or conceptual map of the graph. This will help you visualize the problem and decide which algorithm to use. Familiarity with common graph problems, such as finding connected components or detecting cycles, will also improve your ability to solve these problems under time constraints.