可达矩阵

可达矩阵"/>

可达矩阵

参考1
自定义输入矩阵来绘制

根据参考代码，
自定义
代码如下：

# 编程实现有向图连通性的判断
from pylab import mplmpl.rcParams['font.sans-serif'] = ['SimHei']
mpl.rcParams['axes.unicode_minus'] = False
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
import pylab#定义x三阶矩阵
x = np.array([[1, 0, 0], [1, 1, 0], [1, 1, 1]])#随机生成x为五阶矩阵
# x = np.random.randint(0, 2, (5, 5))
n = len(x)value_1 = value_2 = sum_1 = sum_2 = sum_3 = sum_4 = y = final = x
y = x + x.T# 计算可达矩阵
for i in range(1, n):value_1 = np.matmul(value_1, x)sum_1 = sum_1 + value_1
sum_2 = sum_1 + np.identity(n)reachability_matrix = sum_2 > 0.5print("此有向图的可达矩阵为：")
print(reachability_matrix.astype(int))final = reachability_matrix + reachability_matrix.Tfor i in range(1, n):value_2 = np.matmul(value_2, y)sum_3 = sum_3 + value_2
sum_4 = sum_3 + np.identity(n)
reachability_matrix_1 = sum_4 > 0.5# 给出判断结果
if ((reachability_matrix.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G为强连通图或其为无向连通图")
elif ((final.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G是单向连通图")
elif ((reachability_matrix_1.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G是弱连通图")
else:print("此有向图不连通")# 下面展示图形化输出有向图G
G = nx.DiGraph()
for i in range(0, n):j=i+1G.add_node(i, desc='p' + str(j))for p in range(0, n):for q in range(0, n):if x[p, q] == 1:G.add_edges_from([(p, q)], weight='1')edge_labels = dict([((u, v), d['weight']) for u, v, d in G.edges(data=True)])
edge_colors = ['black']
pos = nx.spring_layout(G)
node_labels = nx.get_node_attributes(G, 'desc')
nx.draw_networkx_labels(G, pos, labels=node_labels)
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
nx.draw(G, pos, node_size=1500, edge_color=edge_colors, edge_cmap=plt.cm.Reds)
plt.title('Directed Graph', fontsize=10)
pylab.show()

第二版

增大了字体
可以自定义字体大小

# 编程实现有向图连通性的判断
from pylab import mplmpl.rcParams['font.sans-serif'] = ['SimHei']
mpl.rcParams['axes.unicode_minus'] = False
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
import pylab#定义x三阶矩阵
x = np.array([[1, 0, 0], [1, 1, 0], [1, 1, 1]])#随机生成x为五阶矩阵
# x = np.random.randint(0, 2, (5, 5))
n = len(x)value_1 = value_2 = sum_1 = sum_2 = sum_3 = sum_4 = y = final = x
y = x + x.T# 计算可达矩阵
for i in range(1, n):value_1 = np.matmul(value_1, x)sum_1 = sum_1 + value_1
sum_2 = sum_1 + np.identity(n)reachability_matrix = sum_2 > 0.5print("此有向图的可达矩阵为：")
print(reachability_matrix.astype(int))final = reachability_matrix + reachability_matrix.Tfor i in range(1, n):value_2 = np.matmul(value_2, y)sum_3 = sum_3 + value_2
sum_4 = sum_3 + np.identity(n)
reachability_matrix_1 = sum_4 > 0.5# 给出判断结果
if ((reachability_matrix.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G为强连通图或其为无向连通图")
elif ((final.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G是单向连通图")
elif ((reachability_matrix_1.astype(int) == np.ones((n, n)).astype(int)).all()):print("此有向线图G是弱连通图")
else:print("此有向图不连通")# 下面展示图形化输出有向图G
G = nx.DiGraph()
for i in range(0, n):j = i + 1G.add_node(i, desc='p' + str(j))for p in range(0, n):for q in range(0, n):if x[p, q] == 1:G.add_edges_from([(p, q)], weight='1')edge_labels = dict([((u, v), d['weight']) for u, v, d in G.edges(data=True)])
edge_colors = ['black']
pos = nx.spring_layout(G)
node_labels = nx.get_node_attributes(G, 'desc')
nx.draw_networkx_labels(G, pos, labels=node_labels, font_size=16)  # 设置字体大小为16nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_size=12)nx.draw(G, pos, node_size=1500, edge_color=edge_colors, edge_cmap=plt.cm.Reds)
plt.title('Directed Graph', fontsize=10)
pylab.show()