介数中心性快速计算

Posted 2021-05-30 My_serendipity

介数中心性快速计算

1. 直接调用networkx
   2001年brandes提出的算法”A faster algorithm for betweenness centrality”
   networkx计算网络的介数中心性

import networkx as nx
G=nx.DiGraph()   # 有向图
# score = nx.betweenness_centrality(G)
# b = nx.betweenness_centrality(G)
for v in G.nodes():
	# print("%0.2d %5.3f" % (v, b[v]))
	print(v)
2. 2001年brandes提出算法 : A faster algorithm for betweenness centrality

import networkx as nx
from queue import Queue
G = nx.read_gml("dodepend_10_t1.gml")

algorithm from networkx

C = nx.centrality.betweenness_centrality(G,normalized=False)

CB = dict.fromkeys(G,0.0)
for s in G.nodes():
Pred = {w:[] for w in G.nodes()}
dist = dict.fromkeys(G,None)
sigma = dict.fromkeys(G,0.0)
dist[s] = 0
sigma[s] = 1
Q = Queue()
Q.put(s)
S = []
while not Q.empty():
v = Q.get()
S.append(v)
for w in G.neighbors(v):
if dist[w] == None:
dist[w] = dist[v] + 1
Q.put(w)
if dist[w] == dist[v] + 1:
sigma[w] += sigma[v]
Pred[w].append(v)
delta = dict.fromkeys(G,0.0)
for w in S[::-1]:
for v in Pred[w]:
delta[v] += sigma[v]/sigma[w]*(1+delta[w])
if w != s:
CB[w] += delta[w]
for v in CB:
CB[v] /= 2.0

compare with networkx\'s implements

print(sum(abs(CB[v]-C[v]) for v in G))

for v in G:
print(v)
print(abs(CB[v]-C[v]))
无向图（验证与networkx结果相差28倍）

3. 
![](https://img2020.cnblogs.com/blog/1990899/202105/1990899-20210530183334194-906166522.png)