Is that something we can't accomplish with some other representation?
Edge list and adjacency list represent the same thing so if you can do something with one, you can do it with the other. In the worst case, you will have to convert one to the other.
When it comes to space, storing edge lists takes up less space than adjacency lists in most cases. For example, the adjacency list will take up less space for an undirected graph with high degree vertices.
A word about space complexity. We say that the space complexity is O(V+E) for the adjacency list and O(E) for the edge list. However, this is misleading. The edge list isn't asymptotically more space-efficient. The adjacency list's space complexity is O(V+E) because it can contain vertices with no edges which is something the edge list cannot do. To make the comparison fair, we should only consider graphs with no 0-degree vertices which can have at most 2E vertices, therefore, the space complexity of the adjacency list becomes O(E) as well.
In my experience, adjacency list is much faster than edge list in most cases. Of course, there will always be exceptions.
The operations where edge list is superior to the adjacency list are typically the ones that directly involve computing something about the edge list itself or straight up returning one. Here is a non-complete list of operations where the edge list is better:
- Getting the list of edges
- Getting the number of edges
For some operations, edge list will be faster but not asymptotically faster.
- Getting the sum of edge weights
- Getting sorted edge weights
In some cases, operations with the edge list are so slow that it is worth converting it into an adjacency list just for that operation. For example, bfs search is O(V+E) time with adjacency list but O(V*E) for edge list because finding the neighbors of a vertex takes considerable time. This case is a tradeoff with space. The space complexity will increase from O(V) to O(E) (or O(V+E) which is the same thing as I discussed earlier.) which is very little next to the time gains.