code: def communicability_exp(G):
      r"""Returns communicability between all pairs of nodes in G.
  
      Communicability between pair of node (u,v) of node in G is the sum of
      walks of different lengths starting at node u and ending at node v.
  
      Parameters
      ----------
      G: graph
  
      Returns
      -------
      comm: dictionary of dictionaries
          Dictionary of dictionaries keyed by nodes with communicability
          as the value.
  
      Raises
      ------
      NetworkXError
          If the graph is not undirected and simple.
  
      See Also
      --------
      communicability:
         Communicability between pairs of nodes in G.
      communicability_betweenness_centrality:
         Communicability betweenness centrality for each node in G.
  
      Notes
      -----
      This algorithm uses matrix exponentiation of the adjacency matrix.
  
      Let G=(V,E) be a simple undirected graph.  Using the connection between
      the powers  of the adjacency matrix and the number of walks in the graph,
      the communicability between nodes u and v is [1]_,
  
      .. math::
          C(u,v) = (e^A)_{uv},
  
      where `A` is the adjacency matrix of G.
  
      References
      ----------
      .. [1] Ernesto Estrada, Naomichi Hatano,
         "Communicability in complex networks",
         Phys. Rev. E 77, 036111 (2008).
         https://arxiv.org/abs/0707.0756
  
      Examples
      --------
      >>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)])
      >>> c = nx.communicability_exp(G)
      """
      import scipy as sp
  
      nodelist = list(G)  # ordering of nodes in matrix
      A = nx.to_numpy_array(G, nodelist)
      # convert to 0-1 matrix
      A[A != 0.0] = 1
      # communicability matrix
      expA = sp.linalg.expm(A)
      mapping = dict(zip(nodelist, range(len(nodelist))))
      c = {}
      for u in G:
          c[u] = {}
          for v in G:
              c[u][v] = float(expA[mapping[u], mapping[v]])
      return c
  
imports: import networkx
  from networkx.utils import not_implemented_for
label_desc: Use image node_id 2 for calling a global function with example usage: communicability_exp(G) and returns: c