def SmallWorldIndex(CIJ):
"""
Computes the small-world index of the graph with connection matrix CIJ.
Self-connections are ignored, as they are cyclic paths.
Inputs:
CIJ -- Graph connectivity matrix. Must be binary (0 or 1) and undirected.
"""
N = len(CIJ)
K = np.sum(np.sum(CIJ)) / len(CIJ) # average degree
# Clustering coefficient
CC = np.mean(clustering_coef_bu(CIJ))
# Distance matrix
[RR, DD] = breadthdist(CIJ)
# Note: the charpath implementation of bctpy is not very robust. Expect
# some warnings. From the output of charpath use only the characteristic
# path length
PL = charpath(DD, include_diagonal=False)[0]
# Calculate small-world index
CCs = CC / (K / N)
PLs = PL / (np.log(N) / np.log(K))
SWI = CCs / PLs
return (SWI)
def SmallWorldIndex(CIJ): """ Computes the small-world index of the graph with connection matrix CIJ. Self-connections are ignored, as they are cyclic paths. Inputs: CIJ -- Graph connectivity matrix. Must be binary (0 or 1) and undirected. """ N = len(CIJ) K = np.sum(np.sum(CIJ))/len(CIJ) # average degree # Clustering coefficient CC = np.mean(clustering_coef_bu(CIJ)) # Distance matrix [RR, DD] = breadthdist(CIJ) # Note: the charpath implementation of bctpy is not very robust. Expect # some warnings. From the output of charpath use only the characteristic # path length PL = charpath(DD, include_diagonal=False)[0] # Calculate small-world index CCs = CC/(K/N) PLs = PL/(np.log(N)/np.log(K)) SWI = CCs/PLs return(SWI)
def test_breadthdist():
x = load_sample(thres=.02)
r, d = bct.breadthdist(x)
d[np.where(np.isinf(d))] = 0
print(np.sum(r), np.sum(d))
assert np.sum(r) == 5804
assert np.sum(d) == 30762
def test_breadthdist():
x = load_sample(thres=.02)
r, d = bct.breadthdist(x)
d[np.where(np.isinf(d))] = 0
print(np.sum(r), np.sum(d))
assert np.sum(r) == 5804
assert np.sum(d) == 30762
def small_world_wu(W):
'''
An implementation of small worldness. Returned is the coefficient cc/lambda,
the ratio of the clustering coefficient to the characteristic path length.
This ratio is >>1 for small world networks.
inputs: W weighted undirected connectivity matrix
output: s small world coefficient
'''
cc = clustering_coef_wu(W)
_, dists = breadthdist(W)
_lambda, _, _, _, _ = charpath(dists)
return np.mean(cc) / _lambda
def small_world_wu(W):
'''
An implementation of small worldness. Returned is the coefficient cc/lambda,
the ratio of the clustering coefficient to the characteristic path length.
This ratio is >>1 for small world networks.
inputs: W weighted undirected connectivity matrix
output: s small world coefficient
'''
cc = clustering_coef_wu(W)
_, dists = breadthdist(W)
_lambda, _, _, _, _ = charpath(dists)
return np.mean(cc) / _lambda
def compute(self):
distance_matrix = bct.breadthdist(self.binarized)[1]
metrics = bct.charpath(distance_matrix)
print("Average Path Length: " + str(metrics[0]))
print("Network Diameter: " + str(metrics[4]))