Remove all symmetrical relations in an adjacency list based on a minimum spanning tree set

So say I have an undirected, weighted graph represented using an adjacency list:

# Dict with key being source and value being list of connections made up of tuple of destination and cost
adjacency_list: dict[int, set[tuple[int, int]]] = {
    1: {(2, 5), (3, 11), (4, 7)},
    2: {(1, 5), (3, 1)},
    3: {(1, 11), (2, 1), (4, 11)},
    4: {(1, 7), (3, 11)},
}

Then an mst set to store the minimum spanning tree:

# Set made up of tuples of source, destination and cost
mst: set[tuple[int, int, int]] = {
    (1, 2, 5),
    (1, 4, 7),
    (2, 3, 1),
}

Is there a way I can remove all symmetrical and equal connections in the mst compared to the adjacency list. For example, remove the connection from 1 to 2 and the one from 2 to 1 in the adjacency list since the connection exists in the mst?

I think first you would need to decide which connection you want to delete.

I guess it's the 2 to 1, leaving only 1 to 2 left.

Then iterate over your mst set.

Find symetry.

Delete it.

for tree_path in mst:
    to_delete = tree_path[1]
    dest, weight = tree_path[0], tree_path[2]

    for al_tree_path in adjacency_list[to_delete]:
        # we've found symetry in adjacency list for a given node
        if al_tree_path == (dest, weight):
            adjacency_list[to_delete].remove(al_tree_path)

That should leave you without symetry in adjacency_list given what was in the mst set.

output for the case you've specified

here's the way to store it as a set of tuples

result = set()
for key, value in adjacency_list.items():
    for tree_path in adjacency_list[key]:
        result.add((key, *tree_path))