networkx 是否具有计算权重的路径长度的功能？

Question

我正在使用 networkx 计算 k 条最短简单路径。 nx.shortest_simple_paths(G, source, target, weight=weight) returns 成本递增的路径列表（考虑权重的累积路径长度）。

我有兴趣获取这些路径的成本。 networkX中有没有简单的函数可以获取这个？

这个问题类似于这个问题：Is there already implemented algorithm in Networkx to return paths lengths along with paths?。

我认为 posted 的回答 post 是错误的。从我提出了以下解决方案（见下文）。

这是正确的方法吗？

networkx 库中有什么简单的东西可用吗？

我的目标是找到k-最短路径的成本。

G = nx.Graph()   # or DiGraph, MultiGraph, MultiDiGraph, etc
G.add_edge('a', 'b', weight=2)
G.add_edge('b', 'c', weight=4)
G.add_edge('a', 'c', weight=10)
G.add_edge('c', 'd', weight=6)
G.size()

def path_length(G, nodes, weight):
    w = 0
    for ind,nd in enumerate(nodes[1:]):
        prev = nodes[ind]
        w += G[prev][nd][weight]
    return w

for path in nx.shortest_simple_paths(G, 'a', 'd', weight='weight'):
    print(path, len(path)) # wrong approach
    print(path, path_length(G,path,'weight')) # correct solution
    print("--------------")

这将输出：

['a', 'b', 'c', 'd'] 4
['a', 'b', 'c', 'd'] 12
--------------
['a', 'c', 'd'] 3
['a', 'c', 'd'] 16
--------------

Answer 1

显然，k_shortest_path 功能尚未在 NetworkX 中实现，即使 demand is not new and you could find some attempt of implementing Yen's algorithm 在网络上也是如此。

您的问题的（非常）粗略的解决方案可能是：

def k_shortest_path(G, source, target, k):
    def path_cost(G, path):
        return sum([G[path[i]][path[i+1]]['weight'] for i in range(len(path)-1)])
    return sorted([(path_cost(G,p), p) for p in nx.shortest_simple_paths(G, source,target,weight='weight') if len(p)==k])[0]

对于这种图表：

import networkx as nx

G = nx.Graph()

G.add_edge('a', 'b', weight=2)
G.add_edge('b', 'c', weight=4)
G.add_edge('a', 'c', weight=10)
G.add_edge('c', 'd', weight=6)
G.add_edge('b', 'd', weight=2)
G.add_edge('b', 'e', weight=5)
G.add_edge('e', 'f', weight=8)
G.add_edge('d', 'f', weight=8)

呼叫：

k_shortest_path(G, 'a', 'f', 4)

returns:

(12, ['a', 'b', 'd', 'f'])

Answer 2

您可以按如下方式使用path_weight(G, path, weight="weight")：

from networkx.algorithms.shortest_paths.generic import shortest_path
from networkx.classes.function import path_weight

path = shortest_path(G, source=source, target=target, weight="weight")
path_length = path_weight(G, path, weight="weight")

Answer 3

我很欣赏@sentence 和@nbeuchat 的解决方案。但是，如果您有一个大图，@sentence 的解决方案会花费很多时间，而 nbeuchat 的解决方案不提供 k 最短路径。我合并他们的解决方案以提出更快的 k 最短简单路径和路径长度。

import networkx as nx

G = nx.Graph()

G.add_edge('a', 'b', weight=2)
G.add_edge('b', 'c', weight=4)
G.add_edge('a', 'c', weight=10)
G.add_edge('c', 'd', weight=6)
G.add_edge('b', 'd', weight=2)
G.add_edge('b', 'e', weight=5)
G.add_edge('e', 'f', weight=8)
G.add_edge('d', 'f', weight=8)

from itertools import islice
from networkx.classes.function import path_weight

def k_shortest_paths(G, source, target, k, weight=None):
    return list(islice(nx.shortest_simple_paths(G, source, target, weight='weight'), k))

for path in k_shortest_paths(G, 'a','f', 3):
    print(path, path_weight(G, path, weight="weight"))

networkx 是否具有计算权重的路径长度的功能？

Does networkx has a function to calculate the length of the path considering weights?

python

python-3.x

networkx

shortest-path

weighted-graph