Networkx Python 中的权重相乘

我正在networkx中绘制一棵树，并添加了百分比份额作为权重。示例：商店和商店的所有者，可以是另一家商店：

import pandas as pd
data = pd.DataFrame({'shop': ['S1', 'S1', 'S1', 'S2', 'S2', 'S3', 'S3', 'S3'],
                     'owner': ['O1', 'O2', 'S2', 'S3', 'O3', 'O4', 'O5', 'O6'],
                     'share': [0.2, 0.2, 0.6, 0.5, 0.5, 0.1, 0.1, 0.8]})
data

 shop   owner   share
 S1      O1     0.2
 S1      O2     0.2
 S1      S2     0.6
 S2      S3     0.5
 S2      O3     0.5
 S3      O4     0.1
 S3      O5     0.1
 S3      O6     0.8

我可以在 networkx 中创建一个有向图，如下所示：

import networkx as nx    
G = nx.from_pandas_edgelist(data,'shop','owner',edge_attr = ('share'), 
create_using=nx.DiGraph())

并绘制结果图：

pos=nx.spring_layout(G, k = 0.5, iterations = 20)
node_labels = {node:node for node in G.nodes()}
nx.draw_networkx(G, pos, labels = node_labels, arrowstyle = '-|>',
             arrowsize = 20,  font_size = 15, font_weight = 'bold')

我如何乘以图表中每个商店的权重，以便获得所有者和百分比份额？像下面这样：

output = pd.DataFrame({'shop': ['S1', 'S1', 'S1', 'S1', 'S1', 'S1', 'S2', 
                                'S2', 'S2','S2', 'S3', 'S3', 'S3'],
                      'owner': ['O1', 'O2', 'O3', 'O4', 'O5', 'O6', 'O3', 
                                'O4', 'O5','O6', 'O4', 'O5', 'O6'],
                      'share': [0.2, 0.2, 0.3, 0.03, 0.03, 0.24, 0.5, 0.05, 
                                0.05, 0.4, 0.1, 0.1, 0.8]})

output

shop    owner   share
 S1     O1      0.2
 S1     O2      0.2
 S1     O3      0.3
 S1     O4      0.03
 S1     O5      0.03
 S1     O6      0.24
 S2     O3      0.5
 S2     O4      0.05
 S2     O5      0.05
 S2     O6      0.4
 S3     O4      0.1
 S3     O5      0.1
 S3     O6      0.8

更新：感谢这个问题here https://stackoverflow.com/questions/47341773/algorithm-to-multiply-edges-of-a-networkx-graph我可以得到任意 2 个选定节点之间的乘积（权重相乘）（见下文），然后如何为数据框中的所有节点获得与上述相同的结果？

start = 'S1' # start node
end = 'O5'   # end node

all_paths = [path for path in nx.all_simple_paths(G, start, end)]

for p in all_paths:                          # keep track of each path
    for _ in range(len(p)):                 # for each node in this path
        pairs = zip(p, p[1:])                    # get sequence of nodes
        product = 1                              
        for pair in pairs:             # for each pair of nodes in this path
            an_edge = G.get_edge_data(pair[0], pair[1])                
            product *= an_edge['share'] 

编辑：误解了问题。这是一个可能的答案：

owners = set(data['owner'])
shops  = set(data['shop'])
summary = {}
for owner in owners:
    for shop in shops:
        paths = list(nx.all_simple_paths(G, shop, owner))
        if len(paths):
            for path in paths:
                for start, end in zip(path[:-1], path[1:]):
                    summary[(shop, owner)] = summary.get((shop,owner), 1) * G[start][end]['share']

summary = pd.DataFrame.from_dict(summary, orient = 'index', columns = 'share'.split())
print(summary)

Output:

           share
(S2, O4)   0.05
(S3, O4)   0.10
(S1, O4)   0.03
(S2, O6)   0.40
(S3, O6)   0.80
(S1, O6)   0.24
(S2, O5)   0.05
(S3, O5)   0.10
(S1, O5)   0.03
(S1, O2)   0.20
(S2, S3)   0.50
(S1, S3)   0.30
(S1, S2)   0.60
(S2, O3)   0.50
(S1, O3)   0.30
(S1, O1)   0.20