论文中的源码在 https://github.com/aditya-grover/node2vec/，python3的话main中的learn_embeddings()需要简单修改以下，然后就能跑通了。
node2vec是基于word2vec的，难点在于Alias Method 抽样算法，其代码的实现比字符串匹配的kmp算法还难以捉摸。
本文加了注释，有助于解析node2vec。
先看使用node2vec的部分：
def read_graph():
'''
Reads the input network in networkx.
'''
if args.weighted:
G = nx.read_edgelist(args.input, nodetype=int, data=(('weight',float),), create_using=nx.DiGraph())
else:
G = nx.read_edgelist(args.input, nodetype=int, create_using=nx.DiGraph())
for edge in G.edges():
G[edge[0]][edge[1]]['weight'] = 1
if not args.directed:
G = G.to_undirected()
return G
def learn_embeddings(walks):
'''
Learn embeddings by optimizing the Skipgram objective using SGD.
'''
walks = [list(map(str, walk)) for walk in walks]
model = Word2Vec(walks, size=args.dimensions, window=args.window_size, min_count=0, sg=1, workers=args.workers, iter=args.iter)
# model.save_word2vec_format(args.output)
model.wv.save_word2vec_format(args.output, binary=False)
return
def main(args):
'''
Pipeline for representational learning for all nodes in a graph.
'''
nx_G = read_graph()
G = node2vec.Graph(nx_G, args.directed, args.p, args.q)
G.preprocess_transition_probs()
walks = G.simulate_walks(args.num_walks, args.walk_length)
learn_embeddings(walks)
if __name__ == "__main__":
args = parse_args()
main(args)然后，都在注释里了：
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:
# 如果序列中仅有一个结点，即第一次游走
# alias_nodes中保存了alias_setup的[alias, accept]，通过alias_draw返回采样的下一个索引号
if len(walk) == 1:
walk.append(cur_nbrs[alias_draw(alias_nodes[cur][0], alias_nodes[cur][1])])
else:
# 当前游走结点的前一个结点和下一个节点
prev = walk[-2]
# 使用alias_edges中记录的[alias, accept]，来采样邻居中的下一个节点
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())
# nodes采样一次为一个epoch，此处就是num_walks个epoch
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.
:return alias_setup(): 在上一次访问顶点 t ，当前访问顶点为 v 时到下一个顶点 x 的未归一化转移概率。
:param src: 随机游走序列种的上一个结点
:param dst: 当前结点
参数p控制重复访问刚刚访问过的顶点的概率。若p较大，则访问刚刚访问过的顶点的概率会变低。
参数q控制着游走是向外还是向内：
若q>1，随机游走倾向于访问和上一次的t接近的顶点(偏向BFS)；若q<1，倾向于访问远离t的顶点(偏向DFS)
'''
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.
用于引导随机游走的预处理，得到马尔可夫转移概率矩阵。
'''
G = self.G
is_directed = self.is_directed
alias_nodes = {}
# G.neighbors(node) 与顶点相邻的所有顶点，更方便更快的访问adjacency字典用: G[cur]
for node in G.nodes():
# 根据邻居节点的权重，计算转移概率
unnormalized_probs = [G[node][nbr]['weight'] for nbr in sorted(G.neighbors(node))]
norm_const = sum(unnormalized_probs)
# 计算当前节点到邻居节点的转移概率，其实就是权重归一化
normalized_probs = [float(u_prob)/norm_const for u_prob in unnormalized_probs]
# 设置alias table，保存每个节点的accept[i]和alias[i]，为后面alias采样做准备。
alias_nodes[node] = alias_setup(normalized_probs)
alias_edges = {}
triads = {}
# 保存每条边的accept[i]和alias[i]
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
:param probs: 指定的采样结果概率分布列表。期望按这个概率列表来采样每个随机变量X。
:return J: alias[i]表示第i列中不是事件i的另一个事件的编号。
:return p: accept[i]表示事件i占第i列矩形的面积的比例。
'''
K = len(probs)
# q表示：accept数组
q = np.zeros(K)
# J表示：alias数组
J = np.zeros(K, dtype=np.int)
# Alias方法将整个概率分布压成一个 1*N 的矩形，每个事件转换为矩形中的面积。
# 将面积大于1的事件多出的面积补充到面积小于1对应的事件中，以确保每一个小方格的面积为1，
# 同时，保证每一方格至多存储两个事件。
smaller = [] # 面积小于1的事件
larger = [] # 面积大于1的事件
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
# 其实是 q[large] - (1.0 - q[small])，把大的削去(1.0 - q[small])填充到小的上
q[large] = q[large] + q[small] - 1.0
# 大的剩下的面积，放到下一轮继续倒腾
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.
参考：https://zhuanlan.zhihu.com/p/54867139
:param q: accept数组，表示事件i占第i列矩形的面积的比例；
:param J: alias数组，表示alias矩形的第i列中不是事件i的另一个事件的编号，也就是填充的那一列的序号；
生成一个随机数 kk in [0, K]，另一个随机数 x in [0,1],
如果 x < accept[kk]，表示接受事件kk，返回kk，否则拒绝事件kk，返回alias[kk]
'''
K = len(J)
kk = int(np.floor(np.random.rand()*K))
if np.random.rand() < q[kk]:
return kk
else:
return J[kk]
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