其中对应索引：

A ——> 0

B——> 1

C——> 2

D——>3

E——> 4

F——> 5

G——> 6

邻接矩阵表示无向图：

算法思想是通过Dijkstra算法结合自身想法实现的。大致思路是：从起始点开始，搜索周围的路径，记录每个点到起始点的权值存到已标记权值节点字典A，将起始点存入已遍历列表B，然后再遍历已标记权值节点字典A，搜索节点周围的路径，如果周围节点存在于表B，比较累加权值，新权值小于已有权值则更新权值和来源节点，否则什么都不做；如果不存在与表B，则添加节点和权值和来源节点到表A，直到搜索到终点则结束。

这时最短路径存在于表A中，得到终点的权值和来源路径，向上递推到起始点，即可得到最短路径，下面是代码：

# -*-coding:utf-8 -*-
class DijkstraExtendPath():
 def __init__(self, node_map):
 self.node_map = node_map
 self.node_length = len(node_map)
 self.used_node_list = []
 self.collected_node_dict = {}
 def __call__(self, from_node, to_node):
 self.from_node = from_node
 self.to_node = to_node
 self._init_dijkstra()
 return self._format_path()
 def _init_dijkstra(self):
 self.used_node_list.append(self.from_node)
 self.collected_node_dict[self.from_node] = [0, -1]
 for index1, node1 in enumerate(self.node_map[self.from_node]):
 if node1:
 self.collected_node_dict[index1] = [node1, self.from_node]
 self._foreach_dijkstra()
 def _foreach_dijkstra(self):
 if len(self.used_node_list) == self.node_length - 1:
 return
 for key, val in self.collected_node_dict.items(): # 遍历已有权值节点
 if key not in self.used_node_list and key != to_node:
 self.used_node_list.append(key)
 else:
 continue
 for index1, node1 in enumerate(self.node_map[key]): # 对节点进行遍历
 # 如果节点在权值节点中并且权值大于新权值
 if node1 and index1 in self.collected_node_dict and self.collected_node_dict[index1][0] > node1 + val[0]:
 self.collected_node_dict[index1][0] = node1 + val[0] # 更新权值
 self.collected_node_dict[index1][1] = key
 elif node1 and index1 not in self.collected_node_dict:
 self.collected_node_dict[index1] = [node1 + val[0], key]
 self._foreach_dijkstra()
 def _format_path(self):
 node_list = []
 temp_node = self.to_node
 node_list.append((temp_node, self.collected_node_dict[temp_node][0]))
 while self.collected_node_dict[temp_node][1] != -1:
 temp_node = self.collected_node_dict[temp_node][1]
 node_list.append((temp_node, self.collected_node_dict[temp_node][0]))
 node_list.reverse()
 return node_list
def set_node_map(node_map, node, node_list):
 for x, y, val in node_list:
 node_map[node.index(x)][node.index(y)] = node_map[node.index(y)][node.index(x)] = val
if __name__ == "__main__":
 node = ['A', 'B', 'C', 'D', 'E', 'F', 'G']
 node_list = [('A', 'F', 9), ('A', 'B', 10), ('A', 'G', 15), ('B', 'F', 2),
 ('G', 'F', 3), ('G', 'E', 12), ('G', 'C', 10), ('C', 'E', 1),
 ('E', 'D', 7)]
 node_map = [[0 for val in xrange(len(node))] for val in xrange(len(node))]
 set_node_map(node_map, node, node_list)
 # A -->; D
 from_node = node.index('A')
 to_node = node.index('D')
 dijkstrapath = DijkstraPath(node_map)
 path = dijkstrapath(from_node, to_node)
 print path

运行结果：

再来一例：

# -*- coding: utf-8 -*-
import itertools
import re
import math

def combination(lst): #全排序
 lists=[]
 liter=itertools.permutations(lst)
 for lts in list(liter):
 lt=''.join(lts)
 lists.append(lt)
 return lists

def coord(lst): #坐标输入
 coordinates=dict()
 print u'请输入坐标：（格式为A:7 17）'
 p=re.compile(r"d+")
 for char in lst:
 str=raw_input(char+':')
 dot=p.findall(str)
 coordinates[char]=[dot[0],dot[1]]
 print coordinates
 return coordinates

def repeat(lst): #删除重复组合
 for ilist in lst:
 for k in xrange(len(ilist)):
 st=(ilist[k:],ilist[:k])
 strs=''.join(st)
 for jlist in lst:
 if(cmp(strs,jlist)==0):
 lst.remove(jlist)
 for k in xrange(len(ilist)):
 st=(ilist[k:],ilist[:k])
 strs=''.join(st)
 for jlist in lst:
 if(cmp(strs[::-1],jlist)==0):
 lst.remove(jlist)
 lst.append(ilist)
 print lst
 return lst

def count(lst,coordinates): #计算各路径
 way=dict()
 for str in lst:
 str=str+str[:1]
 length=0
 for i in range(len(str)-1):
 x=abs( float(coordinates[str[i]][0]) - float(coordinates[str[i+1]][0]) )
 y=abs( float(coordinates[ str[i] ][1]) - float(coordinates[ str[i+1] ][1]) )
 length+=math.sqrt(x**2+y**2)
 way[str[:len(str)-1]]=length
 return way

if __name__ =="__main__":
 print u'请输入图节点：'
 rlist=list(raw_input())
 coordinates=coord(rlist)

 list_directive = combination(rlist)
# print "有方向完全图所有路径为:",list_directive
# for it in list_directive:
# print it
 print u'有方向完全图所有路径总数:',len(list_directive),"
"

#无方向完全图
 list_directive=repeat(list_directive)
 list_directive=repeat(list_directive)
# print "无方向完全图所有路径为:",list_directive
 print u'无方向完全图所有路径为:'
 for it in list_directive:
 print it
 print u'无方向完全图所有路径总数:',len(list_directive)

 ways=count(list_directive,coordinates)
 print u'路径排序如下：'
 for dstr in sorted(ways.iteritems(), key=lambda d:d[1], reverse = False ):
 print dstr
 raw_input()