How to reverse a graph in linear time?

Question

I know there are two ways to represent my graph: one is using a matrix, and the other one is using a list.

If I use a matrix, I have to flip all the bits in the matrix.

Answer 1

I think reversing the graph by traversing the list takes O(V²), since for each vertex you must add or delete (V-1) edges.

As for Dijkstra's algorithm, as I understand it, if you represent the graph as a matrix or list the algorithm takes O(V²), but some other data structures are faster. The fastest known is a Fibonacci heap, which gives O(E + VlogV).