在Python中使用networkx绘制二部图 [英] Plot bipartite graph using networkx in Python

问题描述

我有一个二部图的n1×n2双邻接矩阵A.矩阵A是scipy.sparse csc矩阵.我想在networkx中使用A绘制二部图.假设节点根据称为node_class的类标签着色.我可以执行以下操作:

import networkx as nx
G = nx.from_numpy_matrix(A)
graph_pos = nx.fruchterman_reingold_layout(G)
degree = nx.degree(G)
nx.draw(G, node_color = node_class, with_labels = False, node_size = [v * 35 for v in degree.values()])

上面的代码适用于正方形密集邻接矩阵.但是不适用于非正方形双邻接矩阵A.错误是:

'Adjacency matrix is not square.'

此外，我拥有的矩阵A是scipy.sparse矩阵，因为它很大并且有很多零.所以我想避免通过堆叠A并添加零来制作(n1 + n2)×(n1 + n2)邻接矩阵.

我检查了NetworkX的二部图文档，但没有提到如何使用双邻接矩阵绘制二部图，或如何使用双邻接稀疏矩阵创建图.如果有人可以告诉我如何绘制二部图，那就太好了！

解决方案

我不相信有一个NetworkX函数可以根据偏差矩阵创建图，因此您必须编写自己的图. (但是，它们确实有一个双向模块您应该检查

这里是定义一个函数的一种方法，该函数采用一个稀疏的邻接矩阵并将其转换为NetworkX图(请参阅注释以获取解释).

# Input: M scipy.sparse.csc_matrix
# Output: NetworkX Graph
def nx_graph_from_biadjacency_matrix(M):
    # Give names to the nodes in the two node sets
    U = [ "u{}".format(i) for i in range(M.shape[0]) ]
    V = [ "v{}".format(i) for i in range(M.shape[1]) ]

    # Create the graph and add each set of nodes
    G = nx.Graph()
    G.add_nodes_from(U, bipartite=0)
    G.add_nodes_from(V, bipartite=1)

    # Find the non-zero indices in the biadjacency matrix to connect 
    # those nodes
    G.add_edges_from([ (U[i], V[j]) for i, j in zip(*M.nonzero()) ])

    return G

请参阅下面的示例用例，其中我使用 nx.complete_bipartite_graph 以生成完整的图形:

import networkx as nx, numpy as np
from networkx.algorithms import bipartite
from scipy.sparse import csc_matrix
import matplotlib.pyplot as plt
RB = nx.complete_bipartite_graph(3, 2)
A  = csc_matrix(bipartite.biadjacency_matrix(RB, row_order=bipartite.sets(RB)[0]))
G = nx_graph_from_biadjacency_matrix(A)
nx.draw_circular(G, node_color = "red", with_labels = True)
plt.show()

这是输出图:

I have an n1-by-n2 bi-adjacency matrix A of a bipartite graph. The matrix A is a scipy.sparse csc matrix. I would like to plot the bipartite graph using A in networkx. Assume that the nodes are colored according to their class labels called node_class. I could do the following:

import networkx as nx
G = nx.from_numpy_matrix(A)
graph_pos = nx.fruchterman_reingold_layout(G)
degree = nx.degree(G)
nx.draw(G, node_color = node_class, with_labels = False, node_size = [v * 35 for v in degree.values()])

The above code works fine for a square dense adjacency matrix. However not for a non-square bi-adjacency matrix A. The error is:

'Adjacency matrix is not square.'

Moreover the matrix A I have is a scipy.sparse matrix` because it is very large and have lots of zeros. So I would want to avoid making an (n1+n2)-by-(n1+n2) adjacency matrix by stacking A and adding zeros.

I checked the documentation of NetworkX for bipartite graphs, it does not mention how to plot bi-partite graph using bi-adjacency matrix, or create a graph using bi-adjacency sparse matrix. If someone could tell me how to plot the bipartite graph, that would be great!

解决方案

I don't believe there is a NetworkX function that creates a graph from a biadjacency matrix, so you'll have to write your own. (However, they do have a bipartite module you should check out.)

Here's one way to define a function that takes a sparse biadjacency matrix and converts it to a NetworkX graph (see the comments for explanation).

# Input: M scipy.sparse.csc_matrix
# Output: NetworkX Graph
def nx_graph_from_biadjacency_matrix(M):
    # Give names to the nodes in the two node sets
    U = [ "u{}".format(i) for i in range(M.shape[0]) ]
    V = [ "v{}".format(i) for i in range(M.shape[1]) ]

    # Create the graph and add each set of nodes
    G = nx.Graph()
    G.add_nodes_from(U, bipartite=0)
    G.add_nodes_from(V, bipartite=1)

    # Find the non-zero indices in the biadjacency matrix to connect 
    # those nodes
    G.add_edges_from([ (U[i], V[j]) for i, j in zip(*M.nonzero()) ])

    return G

See an example use case below, where I use nx.complete_bipartite_graph to generate a complete graph:

import networkx as nx, numpy as np
from networkx.algorithms import bipartite
from scipy.sparse import csc_matrix
import matplotlib.pyplot as plt
RB = nx.complete_bipartite_graph(3, 2)
A  = csc_matrix(bipartite.biadjacency_matrix(RB, row_order=bipartite.sets(RB)[0]))
G = nx_graph_from_biadjacency_matrix(A)
nx.draw_circular(G, node_color = "red", with_labels = True)
plt.show()

And here's the output graph:

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