code: def unconstrained_one_edge_augmentation(G):
      """Finds the smallest set of edges to connect G.
  
      This is a variant of the unweighted MST problem.
      If G is not empty, a feasible solution always exists.
  
      Parameters
      ----------
      G : NetworkX graph
         An undirected graph.
  
      Yields
      ------
      edge : tuple
          Edges in the one-edge-augmentation of G
  
      See Also
      --------
      :func:`one_edge_augmentation`
      :func:`k_edge_augmentation`
  
      Examples
      --------
      >>> G = nx.Graph([(1, 2), (2, 3), (4, 5)])
      >>> G.add_nodes_from([6, 7, 8])
      >>> sorted(unconstrained_one_edge_augmentation(G))
      [(1, 4), (4, 6), (6, 7), (7, 8)]
      """
      ccs1 = list(nx.connected_components(G))
      C = collapse(G, ccs1)
      # When we are not constrained, we can just make a meta graph tree.
      meta_nodes = list(C.nodes())
      # build a path in the metagraph
      meta_aug = list(zip(meta_nodes, meta_nodes[1:]))
      # map that path to the original graph
      inverse = defaultdict(list)
      for k, v in C.graph["mapping"].items():
          inverse[v].append(k)
      for mu, mv in meta_aug:
          yield (inverse[mu][0], inverse[mv][0])
  
imports: import itertools
  import math
  from collections import defaultdict, namedtuple
  import networkx
  from networkx.utils import not_implemented_for, py_random_state
label_desc: Use image node_id 10 for calling a global function with example usage: unconstrained_one_edge_augmentation(G) without return types