code: def _auxiliary_graph(G, Features):
      """
      prepare a graph with twice the number of vertices
      this graph will contain the connectivity information
      along the merges.
      """
      K = WeightedGraph(2 * G.V - 1)
      K.E = G.E
      K.edges = G.edges.copy()
      K.weights = np.ones(K.E)
      K.symmeterize()
      if K.E > 0:
          valid = K.edges[:, 0] < K.edges[:, 1]
          K.remove_edges(valid)
      #
      K.remove_trivial_edges()
      _initial_inertia(K, Features)
      return K
  
imports: from warnings import warn
  import numpy
  from ..graph.forest import Forest
  from ..graph.graph import WeightedGraph
label_desc: Use image node_id 7 for calling a global function with example usage: _auxiliary_graph(G, Features) and returns: K