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node2vec.py
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import numpy as np
import networkx as nx
import random
class Graph():
def __init__(self, nx_G, is_directed, p, q):
self.G = nx_G
self.is_directed = is_directed
self.p = p
self.q = q
def node2vec_walk(self, walk_length, start_node):
'''
Simulate a random walk starting from start node.
'''
G = self.G
alias_nodes = self.alias_nodes
alias_edges = self.alias_edges
walk = [start_node]
while len(walk) < walk_length:
cur = walk[-1]
cur_nbrs = sorted(G.neighbors(cur))
if len(cur_nbrs) > 0:
if len(walk) == 1:
walk.append(cur_nbrs[alias_draw(alias_nodes[cur][0], alias_nodes[cur][1])])
else:
prev = walk[-2]
next = cur_nbrs[alias_draw(alias_edges[(prev, cur)][0],
alias_edges[(prev, cur)][1])]
walk.append(next)
else:
break
return walk
def simulate_walks(self, num_walks, walk_length):
'''
Repeatedly simulate random walks from each node.
'''
G = self.G
walks = []
nodes = list(G.nodes())
print('Walk iteration:')
for walk_iter in range(num_walks):
print(str(walk_iter+1), '/', str(num_walks))
random.shuffle(nodes)
for node in nodes:
walks.append(self.node2vec_walk(walk_length=walk_length, start_node=node))
return walks
def get_alias_edge(self, src, dst):
'''
Get the alias edge setup lists for a given edge.
'''
G = self.G
p = self.p
q = self.q
unnormalized_probs = []
for dst_nbr in sorted(G.neighbors(dst)):
if dst_nbr == src:
unnormalized_probs.append(G[dst][dst_nbr]['weight']/p)
elif G.has_edge(dst_nbr, src):
unnormalized_probs.append(G[dst][dst_nbr]['weight'])
else:
unnormalized_probs.append(G[dst][dst_nbr]['weight']/q)
norm_const = sum(unnormalized_probs)
normalized_probs = [float(u_prob)/norm_const for u_prob in unnormalized_probs]
return alias_setup(normalized_probs)
def preprocess_transition_probs(self):
'''
Preprocessing of transition probabilities for guiding the random walks.
'''
G = self.G
is_directed = self.is_directed
alias_nodes = {}
for node in G.nodes():
unnormalized_probs = [G[node][nbr]['weight'] for nbr in sorted(G.neighbors(node))]
norm_const = sum(unnormalized_probs)
normalized_probs = [float(u_prob)/norm_const for u_prob in unnormalized_probs]
alias_nodes[node] = alias_setup(normalized_probs)
alias_edges = {}
triads = {}
if is_directed:
for edge in G.edges():
alias_edges[edge] = self.get_alias_edge(edge[0], edge[1])
else:
for edge in G.edges():
alias_edges[edge] = self.get_alias_edge(edge[0], edge[1])
alias_edges[(edge[1], edge[0])] = self.get_alias_edge(edge[1], edge[0])
self.alias_nodes = alias_nodes
self.alias_edges = alias_edges
return
def alias_setup(probs):
'''
Compute utility lists for non-uniform sampling from discrete distributions.
Refer to https://hips.seas.harvard.edu/blog/2013/03/03/the-alias-method-efficient-sampling-with-many-discrete-outcomes/
for details
'''
K = len(probs)
q = np.zeros(K)
J = np.zeros(K, dtype=np.int)
smaller = []
larger = []
for kk, prob in enumerate(probs):
q[kk] = K*prob
if q[kk] < 1.0:
smaller.append(kk)
else:
larger.append(kk)
while len(smaller) > 0 and len(larger) > 0:
small = smaller.pop()
large = larger.pop()
J[small] = large
q[large] = q[large] + q[small] - 1.0
if q[large] < 1.0:
smaller.append(large)
else:
larger.append(large)
return J, q
def alias_draw(J, q):
'''
Draw sample from a non-uniform discrete distribution using alias sampling.
'''
K = len(J)
kk = int(np.floor(np.random.rand()*K))
if np.random.rand() < q[kk]:
return kk
else:
return J[kk]