请给出输出所有边被最短路径使用次数的完整代码

完整代码如下：

import pandas as pd 
import numpy as np 
import networkx as nx 
import matplotlib.pyplot as plt  

df = pd.read_excel(r"C:\Users\li'yi'jie\Desktop\运筹学网络规划数据.xlsx") 
edges = [] 
for i in range(len(df)): 
    edge = { 
        "id": df.loc[i, "边的编号"], 
        "tail": df.loc[i, "边的尾节点"], 
        "head": df.loc[i, "边的头节点"], 
        "length": df.loc[i, "长度"], 
        "capacity": df.loc[i, "容量"] 
    } 
    edges.append(edge) 

plt.figure(figsize=(15,15)) 
G = nx.DiGraph() 
for edge in edges: 
    G.add_edge(edge["tail"], edge["head"], weight=edge["length"]) 

pos = nx.spring_layout(G) 
nx.draw(G, pos, with_labels=True) 
labels = nx.get_edge_attributes(G, "weight") 
nx.draw_networkx_edge_labels(G, pos, edge_labels=labels, label_pos=0.5) 
plt.show() 

all_pairs = dict(nx.all_pairs_dijkstra_path_length(G)) 
rows = [] 
for start_node, dist_dict in all_pairs.items(): 
    for end_node, dist in dist_dict.items(): 
        rows.append({'起始节点': start_node, '终止节点': end_node, '最短路径长度': dist}) 

df_result = pd.DataFrame(rows) 
df_result.to_excel('all_pairs.xlsx', index=False) 

# 计算每个节点到其他节点的平均最短距离 
avg_dists = [] 
for node in G.nodes(): 
    dist_sum = 0 
    for dist in all_pairs[node].values(): 
        dist_sum += dist 
    avg_dist = dist_sum / len(G.nodes()) 
    avg_dists.append(avg_dist) 

# 画柱状图 
plt.figure(figsize=(15,15)) 
plt.bar(G.nodes(), avg_dists) 
plt.title("每个节点到其他节点的平均最短距离") 
plt.xlabel("节点") 
plt.ylabel("平均最短距离") 
plt.show() 

# 计算每条边被最短路径使用的次数 
all_paths = dict(nx.all_pairs_dijkstra_path(G)) 
edge_counts = {edge["id"]: 0 for edge in edges} 
for start_node in all_paths: 
    for end_node in all_paths[start_node]: 
        path = all_paths[start_node][end_node] 
        for i in range(len(path) - 1): 
            edge_id = G[path[i]][path[i+1]]["id"] 
            edge_counts[edge_id] += 1 

# 输出每条边被最短路径使用的次数 
for edge in edges: 
    print("边{}被使用了{}次".format(edge["id"], edge_counts[edge["id"]])) 

这段代码在计算完所有节点对之间的最短路径后，遍历所有路径上的边，统计每条边被使用的次数，并输出每条边被使用的次数。