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# Source code for networkx.algorithms.bipartite.spectral

    """
    Spectral bipartivity measure.
    """

    import networkx as nx

    __all__ = ["spectral_bipartivity"]

    @nx._dispatchable(edge_attrs="weight")
    def spectral_bipartivity(G, nodes=None, weight="weight"):
        """Returns the spectral bipartivity.

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

        nodes : list or container  optional(default is all nodes)
          Nodes to return value of spectral bipartivity contribution.

        weight : string or None  optional (default = 'weight')
          Edge data key to use for edge weights. If None, weights set to 1.

        Returns
        -------
        sb : float or dict
           A single number if the keyword nodes is not specified, or
           a dictionary keyed by node with the spectral bipartivity contribution
           of that node as the value.

        Examples
        --------
        >>> from networkx.algorithms import bipartite
        >>> G = nx.path_graph(4)
        >>> bipartite.spectral_bipartivity(G)
        1.0

        Notes
        -----
        This implementation uses Numpy (dense) matrices which are not efficient
        for storing large sparse graphs.

        See Also
        --------
        color

        References
        ----------
        .. [1] E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of
           bipartivity in complex networks", PhysRev E 72, 046105 (2005)
        """
        import scipy as sp

        nodelist = list(G)  # ordering of nodes in matrix
        A = nx.to_numpy_array(G, nodelist, weight=weight)
        expA = sp.linalg.expm(A)
        expmA = sp.linalg.expm(-A)
        coshA = 0.5 * (expA + expmA)
        if nodes is None:
            # return single number for entire graph
            return float(coshA.diagonal().sum() / expA.diagonal().sum())
        else:
            # contribution for individual nodes
            index = dict(zip(nodelist, range(len(nodelist))))
            sb = {}
            for n in nodes:
                i = index[n]
                sb[n] = coshA.item(i, i) / expA.item(i, i)
            return sb