def METHOD_NAME(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