我有一个 networkx 图，代表大约 100 万个对象(顶点)的最小生成树。我想知道是否有一种有效的方法可以找到给定顶点与许多其他顶点之一之间的最短路径。
这是一个顶点数较少 (110) 的示例图
nodes = [(0.0, {'label': 2}) ,
(1.0, {'label': 2}) ,
(2.0, {'label': 0}) ,
(3.0, {'label': 2}) ,
(4.0, {'label': 2}) ,
(5.0, {'label': 0}) ,
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(85.0, {'label': 0}) ,
(86.0, {'label': 1}) ,
(87.0, {'label': 2}) ,
(88.0, {'label': 1}) ,
(89.0, {'label': 0}) ,
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(92.0, {'label': 0}) ,
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(106.0, {'label': -1}) ,
(107.0, {'label': 1}) ,
(108.0, {'label': 0}) ,
(109.0, {'label': -1})]
edges = [(0.0, 25.0, {'weight': 1.3788141613435239}) ,
(0.0, 15.0, {'weight': 1.1948288781935414}) ,
(1.0, 99.0, {'weight': 2.1024875417678257}) ,
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(79.0, 106.0, {'weight': 4.5661761296968333}) ,
(82.0, 95.0, {'weight': 1.083633962514291}) ,
(84.0, 99.0, {'weight': 2.1024875417678257}) ,
(89.0, 92.0, {'weight': 0.75419548272456249}) ,
(100.0, 107.0, {'weight': 2.9259491743365307}) ,
(101.0, 109.0, {'weight': 7.6747981730730297}) ,
(102.0, 108.0, {'weight': 4.3128725576385092}) ,
(104.0, 105.0, {'weight': 7.5515191839631273})]
G2 = nx.Graph()
G2.add_nodes_from(nodes)
G2.add_edges_from(edges)
我想要的是“标签 >= 0 的顶点最接近标签 = -1 的每个顶点”。对于像这样的小图，使用类似 nx.all_pairs_dijkstra_path_length() 然后检查标签的蛮力方法工作正常，但它不能扩展到非常大的图。是否有我可以使用的更高效的算法，尤其是内置到 networkx 中的算法？
更新:
我使用了 Richard 的优秀建议和下面的评论来写这篇文章。我真正想要的是一组标签，我认为这让事情不像 Richard 在 networkx 中提到的那样困惑。整个重新标记在一个数据集上花费了 45 秒，而这需要一个小时才能完成!
def relabel(G, indices_to_relabel):
"""
Update the anomaly labels to be the closest cluster.
"""
# Add a "special" node that has zero weight to all the cluster nodes
print('Adding special node')
G.add_node('special', {'label': 'special'})
special_edges = [(n, 'special', {'weight': 0})
for n, ndat in G.nodes_iter(data=True)
if ndat['label'] != 'special' and ndat['label'] >= 0]
G.add_edges_from(special_edges)
print('Calculating path from special node to all other nodes')
paths = nx.shortest_path(G, source='special', target=None, weight='weight')
print('Updating labels')
new_labels = np.array([ndat['label'] for _, ndat in G.nodes_iter(data=True)])
new_labels[indices_to_relabel] = [G.node[paths[n][1]]['label'] for n in indices_to_relabel]
# Clean up
G.remove_node('special')
return new_labels
最佳答案
我不认为 networkx 中内置了这样的算法，但似乎有一种算法可以扩展成本最低的路径，直到达到某个条件。然而，即使 networkx 不包含这样的功能，构建算法来执行此操作也非常容易。
- 将带有
label==-1的节点称为源节点。 - 将距离源节点最近的
label>=0的节点称为目标节点。我们的目标是找到目标节点。 - 创建一个新节点。这将是特殊节点。
- 将所有潜在的目标节点连接到边权重为 0 的特殊节点。
- 对于每个源节点，找到到特殊节点的最短路径。此路径上的倒数第二个节点必然是目标节点，并且是距离源节点最近的节点。
- 完成后，消除特殊节点及其所有连接边。
如果源节点的数量是S，这个算法运行在O(S(|E|+|V| log |V|))时间(假设最短路径算法是 Dijkstra)。
(可能是我误解了您是希望 -1 最接近 >=0 还是 >=0 最接近 -1。如果我有，只需反转源/目标标签即可。)
#!/usr/bin/env python3
import networkx as nx
nodes = [(0.0, {'label': 2}) ,
(1.0, {'label': 2}) ,
(2.0, {'label': 0}) ,
(3.0, {'label': 2}) ,
(4.0, {'label': 2}) ,
(5.0, {'label': 0}) ,
(6.0, {'label': 0}) ,
(7.0, {'label': 2}) ,
(8.0, {'label': 2}) ,
(9.0, {'label': 1}) ,
(10.0, {'label': 0}) ,
(11.0, {'label': 1}) ,
(12.0, {'label': 1}) ,
(13.0, {'label': 0}) ,
(14.0, {'label': 1}) ,
(15.0, {'label': 2}) ,
(16.0, {'label': 1}) ,
(17.0, {'label': 1}) ,
(18.0, {'label': 2}) ,
(19.0, {'label': 2}) ,
(20.0, {'label': 0}) ,
(21.0, {'label': 1}) ,
(22.0, {'label': 1}) ,
(23.0, {'label': 0}) ,
(24.0, {'label': 1}) ,
(25.0, {'label': 2}) ,
(26.0, {'label': 0}) ,
(27.0, {'label': 0}) ,
(28.0, {'label': 1}) ,
(29.0, {'label': 0}) ,
(30.0, {'label': 2}) ,
(31.0, {'label': 1}) ,
(32.0, {'label': 2}) ,
(33.0, {'label': 1}) ,
(34.0, {'label': 1}) ,
(35.0, {'label': 1}) ,
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(37.0, {'label': 2}) ,
(38.0, {'label': 0}) ,
(39.0, {'label': 0}) ,
(40.0, {'label': 2}) ,
(41.0, {'label': 0}) ,
(42.0, {'label': 1}) ,
(43.0, {'label': 0}) ,
(44.0, {'label': 0}) ,
(45.0, {'label': 2}) ,
(46.0, {'label': 0}) ,
(47.0, {'label': 2}) ,
(48.0, {'label': 0}) ,
(49.0, {'label': 1}) ,
(50.0, {'label': 0}) ,
(51.0, {'label': 1}) ,
(52.0, {'label': 2}) ,
(53.0, {'label': 0}) ,
(54.0, {'label': 1}) ,
(55.0, {'label': 1}) ,
(56.0, {'label': 2}) ,
(57.0, {'label': 1}) ,
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(59.0, {'label': 0}) ,
(60.0, {'label': 2}) ,
(61.0, {'label': 1}) ,
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(63.0, {'label': 2}) ,
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(70.0, {'label': 0}) ,
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(74.0, {'label': 0}) ,
(75.0, {'label': 1}) ,
(76.0, {'label': 1}) ,
(77.0, {'label': 0}) ,
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(80.0, {'label': 2}) ,
(81.0, {'label': 1}) ,
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(106.0, {'label': -1}) ,
(107.0, {'label': 1}) ,
(108.0, {'label': 0}) ,
(109.0, {'label': -1})]
edges = [(0.0, 25.0, {'weight': 1.3788141613435239}) ,
(0.0, 15.0, {'weight': 1.1948288781935414}) ,
(1.0, 99.0, {'weight': 2.1024875417678257}) ,
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(30.0, 95.0, {'weight': 0.78901093530213129}) ,
(31.0, 68.0, {'weight': 0.98851671776185412}) ,
(32.0, 95.0, {'weight': 0.8579399666494596}) ,
(34.0, 54.0, {'weight': 0.55323853417352553}) ,
(34.0, 55.0, {'weight': 0.60906522381767525}) ,
(35.0, 62.0, {'weight': 0.66697239833732958}) ,
(36.0, 93.0, {'weight': 1.2932994772208264}) ,
(37.0, 80.0, {'weight': 0.85527462610640648}) ,
(37.0, 96.0, {'weight': 0.85527462610640648}) ,
(38.0, 46.0, {'weight': 0.95334944284759993}) ,
(39.0, 50.0, {'weight': 0.52028039541706872}) ,
(40.0, 69.0, {'weight': 1.7931323073700682}) ,
(42.0, 62.0, {'weight': 0.51384098628821639}) ,
(42.0, 81.0, {'weight': 0.5466147583189902}) ,
(43.0, 65.0, {'weight': 1.0581157274507453}) ,
(44.0, 108.0, {'weight': 3.0598509599260266}) ,
(44.0, 70.0, {'weight': 1.0805691635112824}) ,
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(46.0, 53.0, {'weight': 1.070516213146298}) ,
(47.0, 78.0, {'weight': 1.2822937333699174}) ,
(47.0, 103.0, {'weight': 3.9053251231648707}) ,
(48.0, 97.0, {'weight': 0.86085201141197409}) ,
(48.0, 67.0, {'weight': 0.75656062694199944}) ,
(49.0, 94.0, {'weight': 1.6216528905308547}) ,
(49.0, 86.0, {'weight': 0.80157999082131093}) ,
(49.0, 62.0, {'weight': 0.7081136236724922}) ,
(51.0, 102.0, {'weight': 1.4704389417937378}) ,
(51.0, 71.0, {'weight': 0.83506431983724716}) ,
(54.0, 75.0, {'weight': 0.70074754481170742}) ,
(55.0, 58.0, {'weight': 0.78571631647476448}) ,
(56.0, 82.0, {'weight': 1.3387438494166808}) ,
(57.0, 84.0, {'weight': 1.558483049272277}) ,
(59.0, 64.0, {'weight': 1.0416266944398496}) ,
(60.0, 98.0, {'weight': 1.2534403896544031}) ,
(63.0, 73.0, {'weight': 0.83646303763566465}) ,
(64.0, 72.0, {'weight': 0.8620326535711742}) ,
(66.0, 77.0, {'weight': 0.79981721989351606}) ,
(67.0, 72.0, {'weight': 0.74002007166874428}) ,
(69.0, 83.0, {'weight': 1.5000235782351021}) ,
(70.0, 77.0, {'weight': 0.75999034076724692}) ,
(71.0, 88.0, {'weight': 0.66450874893016454}) ,
(74.0, 97.0, {'weight': 0.8743417572549379}) ,
(76.0, 107.0, {'weight': 2.0300278349030831}) ,
(77.0, 89.0, {'weight': 0.75999034076724692}) ,
(79.0, 106.0, {'weight': 4.5661761296968333}) ,
(82.0, 95.0, {'weight': 1.083633962514291}) ,
(84.0, 99.0, {'weight': 2.1024875417678257}) ,
(89.0, 92.0, {'weight': 0.75419548272456249}) ,
(100.0, 107.0, {'weight': 2.9259491743365307}) ,
(101.0, 109.0, {'weight': 7.6747981730730297}) ,
(102.0, 108.0, {'weight': 4.3128725576385092}) ,
(104.0, 105.0, {'weight': 7.5515191839631273})]
G2 = nx.Graph()
G2.add_nodes_from(nodes)
G2.add_edges_from(edges)
G2.add_node('special', {'label': 'special'})
special_edges = []
for n, ndat in G2.nodes_iter(data=True):
if ndat['label']!='special' and ndat['label']>=0:
special_edges.append( (n,'special', {'weight':0}) )
G2.add_edges_from(special_edges)
for n, ndat in G2.nodes_iter(data=True):
if ndat['label']==-1:
path = nx.shortest_path(G2, source=n, target='special', weight='weight')
ndat['closest'] = path[-2] #Closest node with label>=0
G2.remove_node('special')
关于python - 找到具有属性的许多节点之一的最短路径，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/41966843/