nodes = ('A', 'B', 'C', 'D', 'E', 'F', 'G', 'H')
distances = {
    'A': {'B': 2, 'C': 1, 'D': 3, 'E': 9, 'F': 4},
    'B': {'C': 4, 'E': 3},
    'C': {'D': 8},
    'D': {'E': 7},
    'E': {'F': 5},
    'F': {'C': 2, 'G': 2, 'H': 2},
    'G': {'F': 1, 'H': 6},
    'H': {'F': 9, 'G': 8}}
unvisited = {node: None for node in nodes}
visited = {}
print(" ")
print("Введите вершину:")
current = input()
currentDistance = 0
unvisited[current] = currentDistance

while True:
    for neighbour, distance in distances[current].items():
        if neighbour not in unvisited: continue
        newDistance = currentDistance + distance
        if unvisited[neighbour] is None or unvisited[neighbour] > newDistance:
            unvisited[neighbour] = newDistance
    visited[current] = currentDistance
    del unvisited[current]
    if not unvisited: break
    candidates = [node for node in unvisited.items() if node[1]]
    if not candidates: break
    current, currentDistance = sorted(candidates, key = lambda x: x[1])[0]


print(visited)

matrix =  [[0,1,1,1,1,1,0,0], # a
     [0,0,1,0,1,0,0,0], # b
     [0,0,0,1,0,0,0,0], # c
     [0,0,0,0,1,0,0,0], # d
     [0,0,0,0,0,1,0,0], # e
     [0,0,1,0,0,0,1,1], # f
     [0,0,0,0,0,1,0,1], # g
     [0,0,0,0,0,1,1,0]] # h

import networkx as nx    #  pip install networkx
import matplotlib.pyplot as plt

distances = {
    'A': {'B': 2, 'C': 1, 'D': 3, 'E': 9, 'F': 4},
    'B': {'C': 4, 'E': 3},
    'C': {'D': 8},
    'D': {'E': 7},
    'E': {'F': 5},
    'F': {'C': 2, 'G': 2, 'H': 2},
    'G': {'F': 1, 'H': 6},
    'H': {'F': 9, 'G': 8}}

G = nx.DiGraph()
for k,v in distances.items():
    for k2,v2 in v.items():
        G.add_edge(k, k2, dist=v2)

In [24]: nx.draw(G, with_labels=True)

In [25]: nx.is_eulerian(G)
Out[25]: False

In [26]: nx.eulerian_circuit(G)
Out[26]: <generator object eulerian_circuit at 0x000000000AD631A8>

In [27]: list(nx.eulerian_circuit(G))
---------------------------------------------------------------------------
NetworkXError                             Traceback (most recent call last)
<ipython-input-27-d4bc2ec5ddbd> in <module>
----> 1 list(nx.eulerian_circuit(G))

~Anaconda3envsmllibsite-packagesnetworkxalgorithmseuler.py in eulerian_circuit(G, source, keys)
    168     """
    169     if not is_eulerian(G):
--> 170         raise nx.NetworkXError("G is not Eulerian.")
    171     if G.is_directed():
    172         G = G.reverse()

NetworkXError: G is not Eulerian.

In [30]: G2 = nx.from_edgelist([('A','B'),('B','C'),('C','D'),('D','A')], create_using=nx.DiGraph)

In [31]: list(nx.eulerian_circuit(G2))
Out[31]: [('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'A')]

In [32]: nx.draw(G2, with_labels=True)