How do different graph representations compare in terms of efficiency?

How do different graph representations compare in terms of efficiency?

Graph representations like adjacency lists and matrices have different efficiencies. Adjacency lists are more space-efficient for sparse graphs, while matrices allow for faster edge lookups.

What about their time complexity for common operations?

For adjacency lists, adding an edge is O(1) on average, while for matrices, it's O(1) as well. However, checking for the existence of an edge is O(V) for lists and O(1) for matrices.

Which representation is better for dense graphs?

For dense graphs, adjacency matrices are generally better because they provide quicker access to edge information, despite using more space.

Can you give an example of when to use each representation?

Sure! Use adjacency lists for sparse graphs like social networks, and adjacency matrices for dense graphs like complete graphs.