如何使用Python NetworkX找到最长的路径? [英] How to find the longest path with Python NetworkX?

问题描述

我有一个从S到T的有向图.

I have a directed graph from S to T.

我想找到路线(S，A，C，E，T)及其容量的总和(1 + 2 + 3 + 1 = 7)，所以总和最大.

And I would like to find the route (S, A, C, E, T) and the sum of its capacities (1 + 2 + 3 + 1 = 7) so the sum is the largest.

我尝试使用networkx.algorithms.flow.ford_fulkerson，但我不知道如何获得从S到T的单向方向.

I tried networkx.algorithms.flow.ford_fulkerson, but I don't know how to get the one-way direction from S to T.

我的环境:

• Ubuntu 12.04
• Python 2.7.8
• NetworkX 1.9
• Matplotlib 1.4.0

example.py

example.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-

import matplotlib.pylab as p
import networkx as nx

if __name__ == '__main__':
    DG = nx.DiGraph()
    DG.add_edge('S', 'a', capacity=1)
    DG.add_edge('a', 'b', capacity=1)
    DG.add_edge('a', 'c', capacity=2)
    DG.add_edge('b', 'd', capacity=1)
    DG.add_edge('b', 'e', capacity=2)
    DG.add_edge('c', 'e', capacity=3)
    DG.add_edge('c', 'f', capacity=2)
    DG.add_edge('d', 'T', capacity=1)
    DG.add_edge('e', 'T', capacity=1)
    DG.add_edge('f', 'T', capacity=1)

    result = nx.algorithms.flow.ford_fulkerson(DG, 'S', 'T')
    print(result.size(weight='capacity')) # 15.0, but I want 7.

    pos = nx.spectral_layout(DG)
    nx.draw(DG, pos)
    nx.draw_networkx_labels(DG, pos)
    nx.draw_networkx_edge_labels(DG, pos)
    p.show()

    # This shows a partly bidirectional graph, which is not what I want.
    pos = nx.spectral_layout(result)
    nx.draw(result, pos)
    nx.draw_networkx_labels(result, pos)
    nx.draw_networkx_edge_labels(result, pos)
    p.show()

推荐答案

负权重适用于约翰逊.您的情况下，修改为:

The negative weights works for johnson. In your case, modified as:

DG = nx.DiGraph()
DG.add_edge('S', 'a', weight=-1)
DG.add_edge('a', 'b', weight=-1)
DG.add_edge('a', 'c', weight=-2)
DG.add_edge('b', 'd', weight=-1)
DG.add_edge('b', 'e', weight=-2)
DG.add_edge('c', 'e', weight=-3)
DG.add_edge('c', 'f', weight=-2)
DG.add_edge('d', 'T', weight=-1)
DG.add_edge('e', 'T', weight=-1)
DG.add_edge('f', 'T', weight=-1)

要找到最长的路径，请使用来获取从S到T的单向方向

To find longest path, get the one-way direction from S to T with

p2 = nx.johnson (DG, weight='weight')
print('johnson: {0}'.format(p2['S']['T']))

结果为:johnson: ['S', 'a', 'c', 'e', 'T']

我的环境:

• 软件版本
• Python 3.4.5 64位[MSC v.1600 64位(AMD64)]
• IPython 5.1.0操作系统Windows 10 10.0.14393
• networkx 1.11

Johnson的Networkx 1.11文档

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