How to get the list of edge values corresponding to all possible paths of a particular length in a graph in Python?

Question

I have the following graph (corresponding edge values are written in the brackets):

L0 -> L1 ('01')
L1 -> L2 ('12')
L1 -> L4 ('14')
L4 -> L5 ('45')
L2 -> L3 ('23')
L3 -> L1 ('31')

Now I want the lists of the edge values of all possible paths of a certain length starting from L0 . So, if length = 3 (excluding starting node), I should get two lists:

['01', '12', '23'] and ['01', '14', '45'].

Traversing in a cycle is allowed. I tried using a 2-level dictionary to represent the graph.

graph = {'L0': {'L1': '01'}, 'L1': {'L2': '12', 'L4': '14'}, 'L2': {'L3': '23'}, 'L3': {'L1': '31'}, 'L4': {'L5': '45'}}

def find_path(graph, start, depth):
    k = 0
    while k < depth:
        a = graph[start]
        for node in graph[start]:
            start = node
        path.append(a[node])
        k+=1 
    return path 
print find_path(graph, 'L0', 4)

Obviously it gives one possible path outputs. But I want all possible ones.

Answer 1

I'd make it recursively progress further, until the limit is hit or it cannot progress further.

# graph: Graph we are operating on
# node: Node we are starting from
# hops: Number of hops we can still do (edges we can take)
def findPaths(graph, node, hops):
    # if no further hops should be done, we were successful and
    # can end the recursion
    if hops == 0:
        yield []
        return

    # if the node is not in the graph, we cannot go further, so
    # the current path is invalid
    if node not in graph:
        return

    # for every node we can reach from the current
    for n in graph[node]:
        # find all paths we can take from here
        for path in findPaths(graph, n, hops - 1):
            # and concat the edge names
            yield [graph[node][n]] + path

Used on your graph (in the given representation) this gives:

>>> list(findPaths(graph, 'L0', 3))
[['01', '14', '45'], ['01', '12', '23']]
>>> list(findPaths(graph, 'L0', 4))
[['01', '12', '23', '31']]
>>> list(findPaths(graph, 'L0', 2))
[['01', '14'], ['01', '12']]

Answer 2

I'd represent it as a simple edge:edge dictionary:

links = {
    0: [1],
    1: [2, 4],
    2: [3],
    4: [5],
    3: [1]
}

Then you can just iterate over it:

def get_all_paths(links, length, start=0):
    paths = [[start]]
    for i in range(length):
        newpaths = []
        for path in paths:
            try:
                for next_node in links[path[-1]]:
                    newpaths.append(path + [next_node])
            except KeyError:
                pass
        paths = newpaths

    return paths

get_all_paths(links, 3)
#>>> [[0, 1, 2, 3], [0, 1, 4, 5]]

Conversion of each [0, 1, 2, 3] to [(0,1), (1,2), (2,3)] can be done in a separate step.

---

It also works with your graph:

links = {'L0': {'L1': '01'}, 'L1': {'L2': '12', 'L4': '14'}, 'L2': {'L3': '23'}, 'L3': {'L1': '31'}, 'L4': {'L5': '45'}}

def get_all_paths(links, length, start=0):
    paths = [[start]]
    for i in range(length):
        newpaths = []
        for path in paths:
            try:
                for next_node in links[path[-1]]:
                    newpaths.append(path + [next_node])
            except KeyError:
                pass
        paths = newpaths

    return paths

get_all_paths(links, 3, start='L0')
#>>> [['L0', 'L1', 'L4', 'L5'], ['L0', 'L1', 'L2', 'L3']]

You can then just convert each path to the ['01', '14', '45'] form.

---

Since you seem to be wondering how to do that last conversion, here's a method:

paths = [['L0', 'L1', 'L4', 'L5'], ['L0', 'L1', 'L2', 'L3']]

def join_paths(paths, links):
    for path in paths:
        yield [links[a][b] for a, b in zip(path, path[1:])]

list(join_paths(paths, links))
#>>> [['01', '14', '45'], ['01', '12', '23']]

zip(path, path[1:]) will turn [1, 2, 3, 4] into [(1, 2), (2, 3), (3, 4)] .

The for a, b in will take each pair and set a and b to the items in it.

The links[a][b] will then look up the path name from the dictionary.

yield returns each item one-at-a-time, so you have to call list on the output of join_paths to get it into a list.