python - 如何用边连接两个子图？

Question

令G1,G2,G3为三个图。每个都有 N[i] 个节点。

让 3x3 矩阵 A 表示不相交图 G1,G2,G3 的节点之间接触的概率。

所以A_ij表示Gi处的节点与Gj处的节点有边的概率。

Aii 将是在 Gi 处的节点之间具有边的概率。

我需要一些帮助来完成此操作，并以这样的方式命名节点，以便在联合图中我将能够看到哪些节点来自哪个 Gi

import networkx as nx
import numpy as np

A = np.array([[0.2, 0.4, 0.2], [0.4, 0.1, 0.5], [0.2, 0.5, 0.3]])
N = [20,30,40]

def get_number_edges(A,N,n):
    return int(A[n-1,n-1]*N[n-1])

G1=nx.dense_gnm_random_graph(N[0],get_number_edges(A,N,1))
G2=nx.dense_gnm_random_graph(N[1],get_number_edges(A,N,2))
G3=nx.dense_gnm_random_graph(N[2],get_number_edges(A,N,3))

C=nx.disjoint_union(nx.disjoint_union(G1,G2),G3)

1. 我不确定如何将节点从 Gi 连接到 Gj，其中 i!=j
2. 我不确定如何使用标签来注释 C 处的节点，以指示这些节点源自哪个图 Gi。

Answer 1

我将首先创建完整的图 C，然后根据需要创建子图。

import itertools
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt

A = np.array([[0.2, 0.4, 0.2], [0.4, 0.1, 0.5], [0.2, 0.5, 0.3]])
N = [20,30,40]

# create a square probability matrix with dimensions (total nodes, total nodes)
# and populate it with the values given in A
indices = []
ctr = 0
for n in N:
    indices.append(list(range(ctr, ctr+n)))
    ctr += n

# TODO: 
# remove this horrible triple loop; 
# have a cold and am not smart enough to do it properly now
total_nodes = sum(N)
probability = np.zeros((total_nodes, total_nodes), dtype=np.float)
for ii, sources in enumerate(indices):
    for jj, targets in enumerate(indices):
        for source, target in itertools.product(sources, targets):
            probability[source, target] = A[ii, jj]
plt.imshow(probability, cmap='gray'); plt.show()

# convert probability matrix into an adjacency matrix
adjacency = probability >= np.random.rand(*probability.shape)
plt.imshow(adjacency, cmap='gray'); plt.show()

# create networkx graph object
C = nx.from_numpy_array(adjacency)

# to get any subgraph, use the indices
G1 = C.subgraph(indices[0])
# etc