def btwns(self):
"""
Find the egocentric betweenness centrality for this node.
"""
ret = 0.0
# Find the neighbors of this node's neighbors.
nbrs = {}
for nbr in self.nbrs():
nbrs[nbr] = nbr.nbrs()
nbrs[self] = self.nbrs()
# We need the node keys sorted properly to build a contact matrix.
snodes = sorted(nbrs.keys())
# Generate a contact matrix.
cmatrix = []
for node1 in snodes:
cmatrix.append([int(node1 != node2 and node1 in nbrs[node2]) for node2 in snodes])
for node1, node2 in combinations(snodes, 2):
row = snodes.index(node1)
col = snodes.index(node2)
if not cmatrix[row][col]:
s = sum(map(mul, cmatrix[row][:], cmatrix[:][col]))
if s > 0:
ret += 1 / float(s)
return ret
def btwns(self, paths):
"""
Find the betweenness centrality for this node.
Key arguments:
paths -- a dictionary of all the shortest paths.
"""
ret = 0.0
for node1, node2 in combinations(paths.keys(), 2):
# There theoretically can be no shortests paths if we deleted
# a bridge, but the density of the new clusters didn't meet the threshold.
if node1 != self and node2 != self and paths[node1][node2]:
# Look at all shortest paths from node1 to node2.
ret += sum([1 for path in paths[node1][node2] if self in path]) / float(len(paths[node1][node2]))
return ret
def cluster_coeff(self):
"""
Find the clustering coefficient.
"""
if len(self.nodes) < 2:
return 0.0
num = 0.0
for node in self.nodes:
# Special case, node with only one neighbor.
if node.deg() < 2:
continue
edges = set()
for nbr1, nbr2 in combinations(node.nbrs(), 2):
edges = edges.union(set(nbr1.edges).intersection(nbr2.edges))
num += (2 * len(edges)) / float(node.deg() * (node.deg() - 1))
return num / len(self.nodes)
def btwns(self, paths):
"""
Find the betweenness centrality for this edge.
Key arguments:
paths -- a dictionary of all the shortest paths.
"""
ret = 0.0
for node1, node2 in combinations(paths.keys(), 2):
# There theoretically can be no shortests paths if we deleted
# a bridge, but the density of the new clusters didn't meet the threshold.
if paths[node1][node2] != None:
# A direct path from one to another still counts as a shortest path.
if len(paths[node1][node2]) == 0:
ret += 1.0
else:
ret += sum([1 for path in paths[node1][node2] if self.node1 in path and self.node2 in path]) / float(len(paths[node1][node2]))
return ret