python - 为什么我得到相同的图表？

Question

我在ipython中使用networkx来分析我的图或网络，当我生成最大生成树和最小生成树时，我得到了一个非常奇怪的结果，这两个图是相同的!这是我的代码如下:

a=nx.maximum_spanning_tree(pearson_net)
b=nx.minimum_spanning_tree(pearson_net)

pearson_net是我原来的网络(图)，我想得到这两个图的边，但是这些边是完全相同的!

a.edges()

这是图 a 的边:

EdgeView([('600000.SH', '600015.SH'), ('600000.SH', '600016.SH'), 
('600000.SH', '600030.SH'), ('600000.SH', '600036.SH'), 
('600000.SH','600109.SH'), ('600000.SH', '600816.SH'), 
('600000.SH','600837.SH'), ('600000.SH', '600999.SH'), 
('600000.SH', '601009.SH'), ('600000.SH', '601099.SH'), 
('600000.SH', '601166.SH'), ('600000.SH', '601288.SH'), 
('600000.SH', '601318.SH'), ('600000.SH', '601328.SH'), 
('600000.SH', '601336.SH'), ('600000.SH', '601377.SH'), 
('600000.SH', '601398.SH'), ('600000.SH', '601555.SH'), 
('600000.SH', '601601.SH'), ('600000.SH', '601628.SH'), 
('600000.SH', '601688.SH'), ('600000.SH', '601788.SH'), 
('600000.SH', '601818.SH'), ('600000.SH', '601939.SH'), 
('600000.SH', '601988.SH'), ('600000.SH', '601998.SH'), 
('600000.SH', '000001.SZ'), ('600000.SH', '000686.SZ'), 
('600000.SH', '000728.SZ'), ('600000.SH', '000750.SZ'), 
('600000.SH', '000776.SZ'), ('600000.SH', '000783.SZ'), 
('600000.SH', '002142.SZ'), ('600000.SH', '002500.SZ'), 
('600000.SH', '002673.SZ')])

然后

b.edges()

这些是图 b 的边:

    EdgeView([('600000.SH', '600015.SH'), ('600000.SH', '600016.SH'), 
('600000.SH', '600030.SH'), ('600000.SH', '600036.SH'), 
('600000.SH','600109.SH'), ('600000.SH', '600816.SH'), 
('600000.SH','600837.SH'), ('600000.SH', '600999.SH'), 
('600000.SH', '601009.SH'), ('600000.SH', '601099.SH'), 
('600000.SH', '601166.SH'), ('600000.SH', '601288.SH'), 
('600000.SH', '601318.SH'), ('600000.SH', '601328.SH'), 
('600000.SH', '601336.SH'), ('600000.SH', '601377.SH'), 
('600000.SH', '601398.SH'), ('600000.SH', '601555.SH'), 
('600000.SH', '601601.SH'), ('600000.SH', '601628.SH'), 
('600000.SH', '601688.SH'), ('600000.SH', '601788.SH'), 
('600000.SH', '601818.SH'), ('600000.SH', '601939.SH'), 
('600000.SH', '601988.SH'), ('600000.SH', '601998.SH'), 
('600000.SH', '000001.SZ'), ('600000.SH', '000686.SZ'), 
('600000.SH', '000728.SZ'), ('600000.SH', '000750.SZ'), 
('600000.SH', '000776.SZ'), ('600000.SH', '000783.SZ'), 
('600000.SH', '002142.SZ'), ('600000.SH', '002500.SZ'), 
('600000.SH', '002673.SZ')])

我无法理解这个结果。为什么maximum_spanning_tree与minimum_spanning_tree相同？

这是 pearson_net 的图表:

它是一个完整的图，一个节点可以与任何其他节点链接。这是下面 pearson_net' 数据集的一部分: 列和索引是图的节点，数字( PIL 逊相关系数)是边的权重。

这是我的完整代码:

pearson_net=nx.Graph()
for i in range(pearson):
   for j in range(i+1,pearson):
     pearson_net.add_edge(pearson.index[i],pearson.columns[j],......
     weights=pearson.iloc[i][j])
tree1=nx.minimum_spanning_tree(pearson_net)
tree2=nx.maximum_spanning_tree(pearson_net)

“pearson”是相关系数的矩阵，即之前的数据集。

Answer 1

测试最小和最大生成树

我们需要使用一个最小的示例来控制 minimum_spanning_tree() 和 maximum_spanning_tree() 函数的结果:

a_mat = [
    [1.,0.661435,0.667419,0.547633],
    [0.661435,1.,0.676438,0.542115],
    [0.667419,0.676438,1.,0.500370],
    [0.547633,0.542115,0.500370,1.]
]
G = nx.from_numpy_matrix(np.array(a_mat))
pos = nx.spring_layout(G)
nx.draw_networkx_nodes(G,pos=pos)
nx.draw_networkx_edges(G,pos=pos)
nx.draw_networkx_edge_labels(G, pos=pos)
plt.axis('off')
plt.show()

从这个例子中，我们可以通过添加最低边权重(0.50037、0.547633、0.542115)轻松找到最小生成树

确实:

mi = nx.minimum_spanning_tree(G)
mi.edges(data=True)

[输出]:

EdgeDataView([(0, 3, {'weight': 0.547633}), (1, 3, {'weight': 0.542115}), (2, 3, {'weight': 0.50037})])

对于最大生成树，我们可以从图中预测最大边权重总和(0.661435, 0.667419,0.547633):

ma = nx.maximum_spanning_tree(G)
ma.edges(data=True)

[输出]:

EdgeDataView([(0, 2, {'weight': 0.667419}), (0, 3, {'weight': 0.547633}), (1, 2, {'weight': 0.676438})])

从这个简单的示例中，我们可以观察到这两个函数的行为符合预期。

如果您向我们展示您的代码，我们也许能够为您发现错误。

[编辑]从数据帧构建图形

从您的更新看来，您的 PIL 逊矩阵是一个 pandas Dataframe。这是从数据帧开始的相同过程。您可以使用networkx专用方法nx.from_pandas_adjacency()。

import pandas as pd
df = pd.DataFrame(a_mat)

创建图表

pearson_net = nx.from_pandas_adjacency(df)

pos = nx.spring_layout(pearson_net)
nx.draw_networkx_nodes(pearson_net,pos=pos)
nx.draw_networkx_edges(pearson_net,pos=pos)
nx.draw_networkx_edge_labels(pearson_net, pos=pos)
plt.axis('off')
plt.show()

[输出]:

调用生成树方法

tree1=nx.minimum_spanning_tree(pearson_net)
tree2=nx.maximum_spanning_tree(pearson_net)

tree1.edges(data=True)

[输出]:

EdgeDataView([(0, 3, {'weight': 0.547633}), (1, 3, {'weight': 0.542115}), (2, 3, {'weight': 0.50037})])

nx.draw_networkx_nodes(tree1,pos=pos)
nx.draw_networkx_edges(tree1,pos=pos)
nx.draw_networkx_edge_labels(tree1, pos=pos)
plt.axis('off')
plt.show()

[输出]:

tree2.edges(data=True)

[输出]:

EdgeDataView([(0, 2, {'weight': 0.667419}), (0, 3, {'weight': 0.547633}), (1, 2, {'weight': 0.676438})])

nx.draw_networkx_nodes(tree2,pos=pos)
nx.draw_networkx_edges(tree2,pos=pos)
nx.draw_networkx_edge_labels(tree2, pos=pos)
plt.axis('off')
plt.show()

[输出]: