72 lines
2 KiB
Python
72 lines
2 KiB
Python
|
"""
|
||
|
|
Spectral bipartivity measure.
|
||
|
|
"""
|
||
|
|
import networkx as nx
|
||
|
|
|
||
|
|
__all__ = ["spectral_bipartivity"]
|
||
|
|
|
||
|
|
|
||
|
|
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)
|
||
|
|
"""
|
||
|
|
try:
|
||
|
|
import scipy.linalg
|
||
|
|
except ImportError as e:
|
||
|
|
raise ImportError(
|
||
|
|
"spectral_bipartivity() requires SciPy: ", "http://scipy.org/"
|
||
|
|
) from e
|
||
|
|
nodelist = list(G) # ordering of nodes in matrix
|
||
|
|
A = nx.to_numpy_array(G, nodelist, weight=weight)
|
||
|
|
expA = scipy.linalg.expm(A)
|
||
|
|
expmA = scipy.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
|