code: def _select_starting_cell(G, starting_edge=None):
      """Select a cell to initiate _find_partition
  
      Parameters
      ----------
      G : NetworkX Graph
      starting_edge: an edge to build the starting cell from
  
      Returns
      -------
      Tuple of vertices in G
  
      Raises
      ------
      NetworkXError
          If it is determined that G is not a line graph
  
      Notes
      -----
      If starting edge not specified then pick an arbitrary edge - doesn't
      matter which. However, this function may call itself requiring a
      specific starting edge. Note that the r, s notation for counting
      triangles is the same as in the Roussopoulos paper cited above.
      """
      if starting_edge is None:
          e = arbitrary_element(G.edges())
      else:
          e = starting_edge
          if e[0] not in G.nodes():
              raise nx.NetworkXError(f"Vertex {e[0]} not in graph")
          if e[1] not in G[e[0]]:
              msg = (
                  f"starting_edge ({e[0]}, {e[1]}) is not in the Graph"
              )
              raise nx.NetworkXError(msg)
      e_triangles = _triangles(G, e)
      r = len(e_triangles)
      if r == 0:
          # there are no triangles containing e, so the starting cell is just e
          starting_cell = e
      elif r == 1:
          # there is exactly one triangle, T, containing e. If other 2 edges
          # of T belong only to this triangle then T is starting cell
          T = e_triangles[0]
          a, b, c = T
          # ab was original edge so check the other 2 edges
          ac_edges = len(_triangles(G, (a, c)))
          bc_edges = len(_triangles(G, (b, c)))
          if ac_edges == 1:
              if bc_edges == 1:
                  starting_cell = T
              else:
                  return _select_starting_cell(G, starting_edge=(b, c))
          else:
              return _select_starting_cell(G, starting_edge=(a, c))
      else:
          # r >= 2 so we need to count the number of odd triangles, s
          s = 0
          odd_triangles = []
          for T in e_triangles:
              if _odd_triangle(G, T):
                  s += 1
                  odd_triangles.append(T)
          if r == 2 and s == 0:
              # in this case either triangle works, so just use T
              starting_cell = T
          elif r - 1 <= s <= r:
              # check if odd triangles containing e form complete subgraph
              triangle_nodes = set()
              for T in odd_triangles:
                  for x in T:
                      triangle_nodes.add(x)
  
              for u in triangle_nodes:
                  for v in triangle_nodes:
                      if u != v and (v not in G[u]):
                          msg = (
                              "G is not a line graph (odd triangles "
                              "do not form complete subgraph)"
                          )
                          raise nx.NetworkXError(msg)
              # otherwise then we can use this as the starting cell
              starting_cell = tuple(triangle_nodes)
  
          else:
              msg = (
                  "G is not a line graph (incorrect number of "
                  "odd triangles around starting edge)"
              )
              raise nx.NetworkXError(msg)
      return starting_cell
  
file_path: networkx/networkx/generators/line.py
imports: from collections import defaultdict
  from functools import partial
  from itertools import combinations
  import networkx
  from networkx.utils import arbitrary_element
  from networkx.utils.decorators import not_implemented_for
label_desc: Use image node_id 8 for calling a global function with example usage: _select_starting_cell(G, starting_edge) and returns: starting_cell, _select_starting_cell, _select_starting_cell