拓扑图的加权最短路径以及边介数的计算python
时间: 2024-04-28 21:03:30 浏览: 23
1. 加权最短路径的计算
可以使用Dijkstra算法或者Bellman-Ford算法来计算加权最短路径。
Dijkstra算法:
```python
import heapq
def dijkstra(graph, start):
distances = {node: float('inf') for node in graph}
distances[start] = 0
pq = [(0, start)]
while pq:
current_distance, current_node = heapq.heappop(pq)
if current_distance > distances[current_node]:
continue
for neighbor, weight in graph[current_node].items():
distance = current_distance + weight
if distance < distances[neighbor]:
distances[neighbor] = distance
heapq.heappush(pq, (distance, neighbor))
return distances
```
其中,graph是一个邻接字典,start是起点,返回值是一个字典,记录了起点到每个节点的最短距离。
Bellman-Ford算法:
```python
def bellman_ford(graph, start):
distances = {node: float('inf') for node in graph}
distances[start] = 0
for _ in range(len(graph) - 1):
for node in graph:
for neighbor, weight in graph[node].items():
if distances[node] + weight < distances[neighbor]:
distances[neighbor] = distances[node] + weight
return distances
```
其中,graph也是一个邻接字典,start是起点,返回值也是一个字典,记录了起点到每个节点的最短距离。
2. 边介数的计算
可以使用networkx库来计算边介数。
```python
import networkx as nx
def edge_betweenness_centrality(graph):
betweenness = nx.edge_betweenness_centrality(graph)
return betweenness
```
其中,graph是一个networkx的图对象,返回值是一个字典,记录了每条边的介数。