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 compute(self):
cc = bct.clustering_coef_bu(self.binarized)
self.stats['CluseringCoefficient'] = [v for v in cc]
average = statistics.mean(self.stats['CluseringCoefficient'])
print("Average Clustering Coefficient: " + str(average) + "\n")
return self.stats
def get_network_measures(fname_connectivity):
C = pd.read_table(fname_connectivity, header=None, dtype=object)
#cleaning up structural data
C = C.drop([0, 1], axis=1)
C = C.drop([0], axis=0)
C = C.iloc[:, :-1]
#C_electrode_names = np.array([e[-4:] for e in np.array(C.iloc[0])])
C = np.array(C.iloc[1:, :]).astype(
'float64') #finally turn into numpy array
#binarize connectivity matrix
C_binarize = bct.weight_conversion(C, "binarize")
#Calculate Network Measures:
# 1. Density
density = bct.density_und(C_binarize)[0]
# 2. Degree
degree_mean = np.mean(bct.degrees_und(C_binarize))
# 3. Clustering Coefficient
clustering_coefficient = bct.clustering_coef_bu(C_binarize)
clustering_coefficient_mean = np.mean(clustering_coefficient)
# 4. characteristic path length (i.e. average shortest path length)
#Get distance
C_dist = bct.distance_bin(C_binarize)
#If there are any disjointed nodes set them equal to the largest non-Inf length
C_dist_max = np.nanmax(
C_dist[C_dist != np.inf]) #find the max length (that's not infinity)
C_dist[np.where(C_dist == np.inf
)] = C_dist_max #find the inifnities, and replace with max
characteristic_path_length = bct.charpath(C_dist)[0]
# 5. Small Worldness
Cr = degree_mean / len(C_binarize)
Lr = np.log10(len(C_binarize)) / np.log10(degree_mean)
gamma = clustering_coefficient_mean / Cr
lamb = characteristic_path_length / Lr
sigma = gamma / lamb
small_worldness = sigma
network_measures = np.zeros(shape=(1, 5))
network_measures[0, :] = [
density, degree_mean, clustering_coefficient_mean,
characteristic_path_length, small_worldness
]
colLabels = [
"Density", "degree_mean", "clustering_coefficient_mean",
"characteristic_path_length", "small_worldness"
]
network_measures_df = pd.DataFrame(network_measures, columns=colLabels)
return network_measures_df
def small_world_bu(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_bu(W)
_, dists = breadthdist(W)
_lambda, _, _, _, _ = charpath(dists)
return np.mean(cc) / _lambda
def small_world_bu(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_bu(W)
_, dists = breadthdist(W)
_lambda, _, _, _, _ = charpath(dists)
return np.mean(cc) / _lambda
def get_network_measures(ifname_connectivity):
C = np.array(pd.DataFrame(loadmat(ifname_connectivity)['connectivity']))
#binarize connectivity matrix
C_binarize = bct.weight_conversion(C, "binarize")
#Calculate Network Measures:
# 1. Density
density = bct.density_und(C_binarize)[0]
# 2. Degree
degree_mean = np.mean(bct.degrees_und(C_binarize))
# 3. Clustering Coefficient
clustering_coefficient = bct.clustering_coef_bu(C_binarize)
clustering_coefficient_mean = np.mean(clustering_coefficient)
# 4. characteristic path length (i.e. average shortest path length)
#Get distance
C_dist = bct.distance_bin(C_binarize)
#If there are any disjointed nodes set them equal to the largest non-Inf length
C_dist_max = np.nanmax(
C_dist[C_dist != np.inf]) #find the max length (that's not infinity)
C_dist[np.where(C_dist == np.inf
)] = C_dist_max #find the inifnities, and replace with max
characteristic_path_length = bct.charpath(C_dist)[0]
# 5. Small Worldness
Cr = degree_mean / len(C_binarize)
Lr = np.log10(len(C_binarize)) / np.log10(degree_mean)
gamma = clustering_coefficient_mean / Cr
lamb = characteristic_path_length / Lr
sigma = gamma / lamb
small_worldness = sigma
network_measures = np.zeros(shape=(1, 5))
network_measures[0, :] = [
density, degree_mean, clustering_coefficient_mean,
characteristic_path_length, small_worldness
]
colLabels = [
"Density", "degree_mean", "clustering_coefficient_mean",
"characteristic_path_length", "small_worldness"
]
network_measures_df = pd.DataFrame(network_measures, columns=colLabels)
return network_measures_df
def calculate_path_and_efficiency_bin(G):
"""
Return the following network metrics for your graph. Uses brain connectivity tool-box.
Input:
G (np.array): binarized matrix, symmetric
Outputs:
Eglob: Global efficiency
average_Elocal: mean Local Efficiency
char_path: Average shortest path length
clustering: Average Clustering coefficient
"""
if not np.allclose(G, G.T):
raise bct.BCTParamError('Not undirected')
average_shortest_path, Eglob, _, _, _ = bct.charpath(bct.distance_bin(G))
average_clustering = np.mean(abs(bct.clustering_coef_bu(G)))
average_Elocal = np.mean(bct.efficiency_bin(G, 1))
return Eglob, average_Elocal, average_clustering, average_shortest_path
def test_cluscoef_bu(): x = bct.binarize(load_sample(thres=.17), copy=False) cc = bct.clustering_coef_bu(x) assert np.allclose(np.sum(cc), 60.10160458)
def test_cluscoef_bu():
x = bct.binarize(load_sample(thres=.17), copy=False)
cc = bct.clustering_coef_bu(x)
assert np.allclose(np.sum(cc), 60.10160458)