1. Implement a program to represent a graph using an adjacency list.
2. Write a function to check if a graph is connected.
3. Create a program to perform Depth First Search (DFS) on a graph.
4. Implement Breadth First Search (BFS) on a graph.
5. Write a function to find the shortest path in an unweighted graph using BFS.
6. Create a program to detect cycles in a directed graph.
7. Implement a function to detect cycles in an undirected graph.
8. Write a program to find all connected components in an undirected graph.
9. Create a program to find the in-degree and out-degree of each vertex in a directed graph.
10. Write a function to perform topological sorting on a directed acyclic graph (DAG).
11. Create a program to find the shortest path in a weighted graph using Dijkstra’s algorithm.
12. Write a function to find the minimum spanning tree (MST) using Prim’s algorithm.
13. Implement Kruskal’s algorithm to find the minimum spanning tree (MST) of a graph.
14. Write a program to determine if a path exists between two vertices in a graph.
15. Create a function to find all bridges in a graph.
16. Implement a function to find articulation points in a graph.
17. Write a program to find the strongly connected components in a directed graph using Tarjan’s algorithm.
18. Create a function to count the number of vertices in a graph.
19. Write a program to count the number of edges in a graph.
20. Implement a function to find the degree of a vertex in a graph.
21. Write a program to check if two graphs are isomorphic.
22. Create a function to represent a graph using an adjacency matrix.
23. Implement a function to perform a graph traversal and print all vertices.
24. Write a program to find the longest path in a directed graph.
25. Create a function to find the shortest path between all pairs of vertices using the Floyd-Warshall algorithm.
26. Write a program to implement a graph using edge list representation.
27. Create a function to remove a vertex from a graph.
28. Write a program to remove an edge from a graph.
29. Implement a function to find the maximum flow in a flow network using the Ford-Fulkerson method.
30. Write a program to find the shortest path using Bellman-Ford algorithm.
31. Create a function to check if a graph is bipartite.
32. Implement a function to find all paths from a source to a destination in a graph.
33. Write a program to find the diameter of a graph.
34. Create a function to find the center of a graph.
35. Write a program to find the connected components of a directed graph.
36. Implement a function to check if a directed graph is acyclic.
37. Create a program to find all cycles in a directed graph.
38. Write a function to calculate the adjacency matrix of a graph.
39. Implement a function to calculate the degree centrality of vertices in a graph.
40. Write a program to check if a graph is a tree.