code: def hoffman_singleton_graph():
      """
      Returns the Hoffman-Singleton Graph.
  
      The Hoffman–Singleton graph is a symmetrical undirected graph
      with 50 nodes and 175 edges.
      All indices lie in ``Z % 5``: that is, the integers mod 5 [1]_.
      It is the only regular graph of vertex degree 7, diameter 2, and girth 5.
      It is the unique (7,5)-cage graph and Moore graph, and contains many
      copies of the Petersen graph [2]_.
  
      Returns
      -------
      G : networkx Graph
          Hoffman–Singleton Graph with 50 nodes and 175 edges
  
      Notes
      -----
      Constructed from pentagon and pentagram as follows: Take five pentagons $P_h$
      and five pentagrams $Q_i$ . Join vertex $j$ of $P_h$ to vertex $h·i+j$ of $Q_i$ [3]_.
  
      References
      ----------
      .. [1] https://blogs.ams.org/visualinsight/2016/02/01/hoffman-singleton-graph/
      .. [2] https://mathworld.wolfram.com/Hoffman-SingletonGraph.html
      .. [3] https://en.wikipedia.org/wiki/Hoffman%E2%80%93Singleton_graph
  
      """
      G = nx.Graph()
      for i in range(5):
          for j in range(5):
              G.add_edge(
                  ("pentagon", i, j), ("pentagon", i, (j - 1) % 5)
              )
              G.add_edge(
                  ("pentagon", i, j), ("pentagon", i, (j + 1) % 5)
              )
              G.add_edge(
                  ("pentagram", i, j), ("pentagram", i, (j - 2) % 5)
              )
              G.add_edge(
                  ("pentagram", i, j), ("pentagram", i, (j + 2) % 5)
              )
              for k in range(5):
                  G.add_edge(
                      ("pentagon", i, j),
                      ("pentagram", k, (i * k + j) % 5),
                  )
      G = nx.convert_node_labels_to_integers(G)
      G.name = "Hoffman-Singleton Graph"
      return G
  
imports: from functools import wraps
  import networkx
  from networkx.exception import NetworkXError
  from networkx.generators.classic import complete_graph, cycle_graph, empty_graph, path_graph
label_desc: Use image node_id 11 for calling a global function with example usage: hoffman_singleton_graph() and returns: G