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+"""
+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