def Q_modularity(network: Network, cluster_mapping: Dict) -> float:
"""Computes the Q-modularity of a network for a given cluster mapping
"""
A = network.adjacency_matrix()
m = network.number_of_edges()
q = 0.0
for v in network.nodes.uids:
for w in network.nodes.uids:
if cluster_mapping[v] == cluster_mapping[w]:
q += A[network.nodes.index[v], network.nodes.index[w]] - \
network.degrees()[v] * network.degrees()[w]/(2*m)
return q/(2*m)
def degree_assortativity(network: Network,
mode: str = 'total',
weight: Weight = None) -> float:
"""Calculates the degree assortativity coefficient of a network.
Parameters
----------
network : Network
The network in which to calculate the Molloy-Reed fraction
"""
A = network.adjacency_matrix(weight=weight)
m = np.sum(A)
d = network.degrees(weight)
if network.directed and mode == 'in':
d = network.indegrees(weight)
elif network.directed and mode == 'out':
d = network.outdegrees(weight)
elif network.directed and mode == 'total':
d = network.degrees(weight)
elif not network.directed:
m = m / 2.
idx = network.nodes.index
cov: float = 0.
var: float = 0.
for i in network.nodes.keys():
for j in network.nodes.keys():
cov += (A[idx[i], idx[j]] - (d[i] * d[j]) / (2 * m)) * d[i] * d[j]
if i != j:
var -= (d[i] * d[j]) / (2 * m) * d[i] * d[j]
else:
var += (d[i] - (d[i] * d[j]) / (2 * m)) * d[i] * d[j]
return cov / var