def edge_current_flow_betweenness_centrality(G, normalized=True,
                                             weight='weight',
                                             dtype=float, solver='full'):
    """Compute current-flow betweenness centrality for edges.

    Current-flow betweenness centrality uses an electrical current
    model for information spreading in contrast to betweenness
    centrality which uses shortest paths.

    Current-flow betweenness centrality is also known as
    random-walk betweenness centrality [2]_.

    Parameters
    ----------
    G : graph
      A NetworkX graph

    normalized : bool, optional (default=True)
      If True the betweenness values are normalized by 2/[(n-1)(n-2)] where
      n is the number of nodes in G.

    weight : string or None, optional (default='weight')
      Key for edge data used as the edge weight.
      If None, then use 1 as each edge weight.

    dtype: data type (float)
      Default data type for internal matrices.
      Set to np.float32 for lower memory consumption.

    solver: string (default='lu')
       Type of linear solver to use for computing the flow matrix.
       Options are "full" (uses most memory), "lu" (recommended), and
       "cg" (uses least memory).

    Returns
    -------
    nodes : dictionary
       Dictionary of edge tuples with betweenness centrality as the value.

    Raises
    ------
    NetworkXError
        The algorithm does not support DiGraphs.
        If the input graph is an instance of DiGraph class, NetworkXError
        is raised.

    See Also
    --------
    betweenness_centrality
    edge_betweenness_centrality
    current_flow_betweenness_centrality

    Notes
    -----
    Current-flow betweenness can be computed in `O(I(n-1)+mn \log n)`
    time [1]_, where `I(n-1)` is the time needed to compute the
    inverse Laplacian.  For a full matrix this is `O(n^3)` but using
    sparse methods you can achieve `O(nm{\sqrt k})` where `k` is the
    Laplacian matrix condition number.

    The space required is `O(nw) where `w` is the width of the sparse
    Laplacian matrix.  Worse case is `w=n` for `O(n^2)`.

    If the edges have a 'weight' attribute they will be used as
    weights in this algorithm.  Unspecified weights are set to 1.

    References
    ----------
    .. [1] Centrality Measures Based on Current Flow.
       Ulrik Brandes and Daniel Fleischer,
       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
       http://www.inf.uni-konstanz.de/algo/publications/bf-cmbcf-05.pdf

    .. [2] A measure of betweenness centrality based on random walks,
       M. E. J. Newman, Social Networks 27, 39-54 (2005).
    """
    from networkx.utils import reverse_cuthill_mckee_ordering
    try:
        import numpy as np
    except ImportError:
        raise ImportError('current_flow_betweenness_centrality requires NumPy ',
                          'http://scipy.org/')
    try:
        import scipy
    except __HOLE__:
        raise ImportError('current_flow_betweenness_centrality requires SciPy ',
                          'http://scipy.org/')
    if G.is_directed():
        raise nx.NetworkXError('edge_current_flow_betweenness_centrality ',
                               'not defined for digraphs.')
    if not nx.is_connected(G):
        raise nx.NetworkXError("Graph not connected.")
    n = G.number_of_nodes()
    ordering = list(reverse_cuthill_mckee_ordering(G))
    # make a copy with integer labels according to rcm ordering
    # this could be done without a copy if we really wanted to
    H = nx.relabel_nodes(G,dict(zip(ordering,range(n))))
    betweenness=(dict.fromkeys(H.edges(),0.0))
    if normalized:
        nb=(n-1.0)*(n-2.0) # normalization factor
    else:
        nb=2.0
    for row,(e) in flow_matrix_row(H, weight=weight, dtype=dtype,
                                   solver=solver):
        pos=dict(zip(row.argsort()[::-1],range(1,n+1)))
        for i in range(n):
            betweenness[e]+=(i+1-pos[i])*row[i]
            betweenness[e]+=(n-i-pos[i])*row[i]
        betweenness[e]/=nb
    return dict(((ordering[s],ordering[t]),float(v))
                for (s,t),v in betweenness.items())


# fixture for nose tests
dataset/ETHPy150Open networkx/networkx/networkx/algorithms/centrality/current_flow_betweenness.py/edge_current_flow_betweenness_centrality