在網絡可靠性中，一種較為經典且在實踐中更為常用的可靠度計算便是二終端可靠度，即給定網絡拓撲結構與邊可靠度（假定節點完全可靠），計算網絡中指定的兩個節點之間的連通可靠度。
import itertools
def min_path_sets(init_matrix,index_start,index_end):
import re
num_point = init_matrix.shape[0]
min_path_list = []
for i in range(num_point-1):
temp = init_matrix**(i+1)
item = expand(temp[index_start-1,index_end-1])
list_given = re.sub('[ *123456789]',"",str(item)).split("+")
#刪除指定階數下，路徑長度不等于階數的路
index_to_delete = []
for j in range(len(list_given)):
if len(list_given[j])!=(i+1) or list_given[j]=='0':
index_to_delete.append(j)
for counter, index in enumerate(index_to_delete):
index = index - counter
list_given.pop(index)
min_path_list.extend(list_given)
return min_path_list
def str_de_duplication(pstr):
a = ''
for i in range(len(pstr)):
if pstr[i] not in a:
a+=pstr[i]
return a
def product_symbol(pstr,my_dict):
import numpy as np
value_list = []
for i in pstr:
value_list.append(my_dict[i])
return np.prod(value_list)
def generate_label(path_sets,my_dict):
import numpy as np
all_result = []
for exp_num in range(len(path_sets)):
item_Combination = list(itertools.combinations(path_sets, exp_num+1))
item_list = list(map(lambda x: str_de_duplication("".join(x)),item_Combination))
value_list = list(map(lambda x: product_symbol(x,my_dict),item_list))
all_result.append(np.sum(value_list)*(-1)**(exp_num))
return np.sum(all_result)
def Matrix_label(init_matrix,my_dict,index_start,index_end):
path_sets = min_path_sets(init_matrix,index_start,index_end)
pro_value = generate_label(path_sets,my_dict)
return pro_value
from sympy import *
from sympy.abc import A,B,C,D,E,F
index_start = 2
index_end = 1
data = Matrix([[0,A,B],
[A,0,C],
[B,C,0]])
my_dict = {'A':0.8,
'B':0.9,
'C':0.9}
Matrix_label(data,my_dict,index_start,index_end)
在前部分，主要定義了幾個函數以便求出最小路集以及利用容斥原理計算二終端可靠度，最終外層函數為Matrix_label(data,my_dict,index_start,index_end)：
