More efficient way of running a random traversal of a directed graph with Networkx

Question

I am trying to simulate a random traversal through a directed networkx graph. The pseudo code is as follows

Create graph G with nodes holding the value true or false. 
// true -> visited, false -> not visited

pick random node N from G
save N.successors as templist
while true
    nooptions = false
    pick random node N from templist
    while N from templist has been visited
        remove N from templist
        pick random node N from templist
        if templist is empty
            nooptions = true
            break
    if nooptions = true 
        break
    save N.successors as templist 

Is there are a more efficient way of marking a path as traveled other than creating a temporary list and removing the elements if they are marked as visited?

EDIT

The goal of the algorithm is to pick a node at random in the graph. Pick a random successor/child of that node. If it is unvisited, go there and mark it as visited. Repeat until there are either no successors/children or there are no unvisited successors/children

Answer 1

Depending on the size of your graph, you could use the built-in all_pairs_shortest_path function. Your function would then be basically:

G = nx.DiGraph()
<add some stuff to G>

# Get a random path from the graph
all_paths = nx.all_pairs_shortest_path(G)

# Choose a random source
source = random.choice(all_paths.keys())
# Choose a random target that source can access
target = random.choice(all_paths[source].keys())
# Random path is at
random_path = all_paths[source][target]

There doesn't appear to be a way to just generate the random paths starting at source that I saw, but the python code is accessible, and adding that feature would be straightforward I think.

Two other possibilities, which might be faster but a little more complicated/manual, would be to use bfs_successors, which does a breadth-first search, and should only include any target node once in the list. Not 100% sure on the format, so it might not be convenient.

You could also generate bfs_tree, which generates a subgraph with no cycles to all nodes that it can reach. That might actually be simpler, and probably shorter?

# Get random source from G.node
source = random.choice(G.node)

min_tree = nx.bfs_tree(G, source)
# Accessible nodes are any node in this list, except I need to remove source.

all_accessible = min_tree.node.keys()
all_accessible.remove(source)
target = random.choice(all_accessible.node.keys())

random_path = nx.shortest_path(G, source, target)