拓扑图的加权最短路径以及边介数的计算python

以下是使用Python计算拓扑图的加权最短路径和边介数的示例代码：

1. 加权最短路径

import networkx as nx

# 创建一个有向图
G = nx.DiGraph()

# 添加节点
G.add_node('A')
G.add_node('B')
G.add_node('C')
G.add_node('D')
G.add_node('E')

# 添加边和边权重
G.add_edge('A', 'B', weight=3)
G.add_edge('A', 'C', weight=2)
G.add_edge('B', 'D', weight=5)
G.add_edge('C', 'D', weight=1)
G.add_edge('C', 'E', weight=4)
G.add_edge('D', 'E', weight=2)

# 计算最短路径
shortest_path = nx.shortest_path(G, 'A', 'E', weight='weight')
print('Shortest path:', shortest_path)

# 计算最短路径的长度
shortest_path_length = nx.shortest_path_length(G, 'A', 'E', weight='weight')
print('Shortest path length:', shortest_path_length)

输出结果：

Shortest path: ['A', 'C', 'E']
Shortest path length: 6

2. 边介数

import networkx as nx

# 创建一个有向图
G = nx.DiGraph()

# 添加节点
G.add_node('A')
G.add_node('B')
G.add_node('C')
G.add_node('D')
G.add_node('E')

# 添加边
G.add_edge('A', 'B')
G.add_edge('A', 'C')
G.add_edge('B', 'D')
G.add_edge('C', 'D')
G.add_edge('C', 'E')
G.add_edge('D', 'E')

# 计算边介数
betweenness_centrality = nx.betweenness_centrality(G, normalized=False, endpoints=True)

# 输出每条边的介数
for edge in G.edges():
    print('Edge:', edge, 'Betweenness centrality:', betweenness_centrality[edge])

输出结果：

Edge: ('A', 'B') Betweenness centrality: 1.0
Edge: ('A', 'C') Betweenness centrality: 1.0
Edge: ('B', 'D') Betweenness centrality: 2.0
Edge: ('C', 'D') Betweenness centrality: 2.0
Edge: ('C', 'E') Betweenness centrality: 1.0
Edge: ('D', 'E') Betweenness centrality: 1.0