# Source code for networkx.algorithms.bipartite.spectral

```"""
Spectral bipartivity measure.
"""
import networkx as nx

__all__ = ["spectral_bipartivity"]

[docs]
@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.

--------
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

```