def __dfsify_branch_uv(u, v, dfs_data):
    """Helper function to convert the output of Bu(v) from edge ids to dfs-ordered fronds."""
    buv = B(u, v, dfs_data)
    new_list = []
    for edge_id in buv:
        edge = dfs_data['graph'].get_edge(edge_id)
        j, k = edge['vertices']
        d_x = D(j, dfs_data)
        d_y = D(k, dfs_data)
        if d_x < d_y:
            smaller = d_x
            larger = d_y
        else:
            smaller = d_y
            larger = d_x
        frond = (smaller, larger)
        new_list.append(frond)
    return new_list
Helper function to convert the output of Bu(v) from edge ids to dfs-ordered fronds.