def clustering_coef_wu(*args): return _bct.clustering_coef_wu(*args)
def clustering_coef_wu(*args):
return _bct.clustering_coef_wu(*args)
def clustering_coef_wu(*args): """clustering_coef_wu(gsl_matrix W) -> gsl_vector""" return _bct.clustering_coef_wu(*args)
def clustering_coef(cmatrix, edgetype, weighted):
""" Clustering coefficient C
For an individual node, the clustering coefficient is defined as the
fraction of the existing number, to the total possible number of
neighbor-neighbor links.
Parameters
----------
cmatrix : connection/adjacency matrix
edgetype : {'directed','undirected'}
weighted : {False, True}
Returns
-------
edgetype == 'undirected':
weighted == True:
C : clustering coefficient C for weighted undirected graph W.
Reference: Onnela et al. 2005, Phys Rev E 71:065103
Mika Rubinov, UNSW, 2007 (last modified July 2008)
weighted == False:
C : clustering coefficient C, for binary undirected graph G
Reference: Watts and Strogatz, 1998, Nature 393:440-442
Mika Rubinov, UNSW, 2007 (last modified September 2008)
edgetype == 'directed':
weighted == True:
C : clustering coefficient C for weighted directed graph W.
Reference: Fagiolo, 2007, Phys Rev E 76:026107
(also see Onnela et al. 2005, Phys Rev E 71:065103);
Mika Rubinov, UNSW, 2007 (last modified July 2008)
See comments for clustering_coef_bd
The weighted modification is as follows:
- The numerator: adjacency matrix is replaced with weights
matrix^1/3
- The denominator: no changes from the binary version
The above reduces to symmetric and/or binary versions of the
clustering coefficient for respective graphs.
weighted == False:
C : clustering coefficient C, for binary directed graph A
Reference: Fagiolo, 2007, Phys Rev E 76:026107.
Mika Rubinov, UNSW, 2007 (last modified July 2008)
In directed graphs, 3 nodes generate up to 8 triangles (2*2*2 edges)
The number of existing triangles is the main diagonal of S^3/2
The number of all (in or out) neighbour pairs is K(K-1)/2
Each neighbour pair may generate two triangles
"False pairs" are i<->j edge pairs (these do not generate triangles)
The number of false pairs is the main diagonal of A^2
Thus the maximum possible number of triangles =
= (2 edges)*([ALL PAIRS] - [FALSE PAIRS]) =
= 2 * (K(K-1)/2 - diag(A^2)) = K(K-1) - 2(diag(A^2))
"""
if edgetype == 'directed':
if weighted:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_wd(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_bd(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
if weighted:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_wu(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_bu(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
def clustering_coef_wu(*args):
"""clustering_coef_wu(gsl_matrix W) -> gsl_vector"""
return _bct.clustering_coef_wu(*args)
def clustering_coef(cmatrix, edgetype, weighted):
""" Clustering coefficient C
For an individual node, the clustering coefficient is defined as the
fraction of the existing number, to the total possible number of
neighbor-neighbor links.
Parameters
----------
cmatrix : connection/adjacency matrix
edgetype : {'directed','undirected'}
weighted : {False, True}
Returns
-------
edgetype == 'undirected':
weighted == True:
C : clustering coefficient C for weighted undirected graph W.
Reference: Onnela et al. 2005, Phys Rev E 71:065103
Mika Rubinov, UNSW, 2007 (last modified July 2008)
weighted == False:
C : clustering coefficient C, for binary undirected graph G
Reference: Watts and Strogatz, 1998, Nature 393:440-442
Mika Rubinov, UNSW, 2007 (last modified September 2008)
edgetype == 'directed':
weighted == True:
C : clustering coefficient C for weighted directed graph W.
Reference: Fagiolo, 2007, Phys Rev E 76:026107
(also see Onnela et al. 2005, Phys Rev E 71:065103);
Mika Rubinov, UNSW, 2007 (last modified July 2008)
See comments for clustering_coef_bd
The weighted modification is as follows:
- The numerator: adjacency matrix is replaced with weights
matrix^1/3
- The denominator: no changes from the binary version
The above reduces to symmetric and/or binary versions of the
clustering coefficient for respective graphs.
weighted == False:
C : clustering coefficient C, for binary directed graph A
Reference: Fagiolo, 2007, Phys Rev E 76:026107.
Mika Rubinov, UNSW, 2007 (last modified July 2008)
In directed graphs, 3 nodes generate up to 8 triangles (2*2*2 edges)
The number of existing triangles is the main diagonal of S^3/2
The number of all (in or out) neighbour pairs is K(K-1)/2
Each neighbour pair may generate two triangles
"False pairs" are i<->j edge pairs (these do not generate triangles)
The number of false pairs is the main diagonal of A^2
Thus the maximum possible number of triangles =
= (2 edges)*([ALL PAIRS] - [FALSE PAIRS]) =
= 2 * (K(K-1)/2 - diag(A^2)) = K(K-1) - 2(diag(A^2))
"""
if edgetype == 'directed':
if weighted:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_wd(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_bd(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
if weighted:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_wu(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)
else:
m = bct.to_gslm(cmatrix.tolist())
str = bct.clustering_coef_bu(m)
strnp = bct.from_gsl(str)
bct.gsl_free(m)
bct.gsl_free(str)
return np.asarray(strnp)