from random import randint

graph = {
    0: [1, 7],
    1: [0, 2],
    2: [1, 3, 4],
    3: [2],
    4: [2],
    5: [6],
    6: [7, 5],
    7: [0, 8, 6],
    8: [7],
}

visited = []

ci = randint(0, 9)
c = graph[ci]
print("Walk starts from node", ci)

moves = 0
path = []
while True:
    if ci not in visited:
        visited.append(ci)
        print("Found node:", ci)
    path.append(ci)

    ci = graph[ci][randint(0, len(graph[ci])-1)]
    moves += 1

    if len(visited) == len(graph):
        break

print("Graph explored in", moves, "steps")