"""
Spectral bipartivity measure.
"""
import networkx as nx
__all__ = ["spectral_bipartivity"]
[docs]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
import scipy.linalg # call as sp.linalg
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 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[i, i] / expA[i, i]
return sb