docs: 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