Find edges in a cycle networkx python

Question

I would like to make an algorithm to find if an edge belongs to a cycle, in an undirected graph, using networkx in Python. I am thinking to use cycle_basis and get all the cycles in the graph. My problem is that cycle_basis returns a list of nodes. How can I convert them to edges?

Answer 1

You can construct the edges from the cycle by connecting adjacent nodes.

In [1]: import networkx as nx

In [2]: G = nx.Graph()

In [3]: G.add_cycle([1,2,3,4])

In [4]: G.add_cycle([10,20,30])

In [5]: basis = nx.cycle_basis(G)

In [6]: basis
Out[6]: [[2, 3, 4, 1], [20, 30, 10]]

In [7]: edges = [zip(nodes,(nodes[1:]+nodes[:1])) for nodes in basis]

In [8]: edges
Out[8]: [[(2, 3), (3, 4), (4, 1), (1, 2)], [(20, 30), (30, 10), (10, 20)]]

Answer 2

Here is my take at it, using just lambda functions (I love lambda functions!):

import networkx as nx

G = nx.Graph()

G.add_cycle([1,2,3,4])

G.add_cycle([10,20,30])

G.add_edge(1,10)


in_path = lambda e, path: (e[0], e[1]) in path or (e[1], e[0]) in path
cycle_to_path = lambda path: list(zip(path+path[:1], path[1:] + path[:1]))
in_a_cycle = lambda e, cycle: in_path(e, cycle_to_path(cycle))
in_any_cycle = lambda e, g: any(in_a_cycle(e, c) for c in nx.cycle_basis(g))

for edge in G.edges():
    print(edge, 'in a cycle:', in_any_cycle(edge, G))

Answer 3

in case you don't find a nice solution, here's an ugly one.

1. with edges() you can get a list of edges that are adjacent to nodes in a cycle. unfortunately, this includes edges adjacent to nodes outside the cycle
2. you can now filter the list of edges by removing those which connect nodes that are not part of the cycle.

please keep us posted if you find a less wasteful solution.

Answer 4

With the help of Aric, and a little trick to check both directions, I finally did this that looks ok.

import networkx as nx

G = nx.Graph()

G.add_cycle([1,2,3,4])

G.add_cycle([10,20,30])

G.add_edge(1,10)


def edge_in_cycle(edge, graph):
    u, v = edge
    basis = nx.cycle_basis(graph)
    edges = [zip(nodes,(nodes[1:]+nodes[:1])) for nodes in basis]
    found = False
    for cycle in edges:
        if (u, v) in cycle or (v, u) in cycle:
            found = True            
    return found

for edge in G.edges():
    print edge, 'in a cycle:', edge_in_cycle(edge, G)

output:

(1, 2) in a cycle: True
(1, 4) in a cycle: True
(1, 10) in a cycle: False
(2, 3) in a cycle: True
(3, 4) in a cycle: True
(10, 20) in a cycle: True
(10, 30) in a cycle: True
(20, 30) in a cycle: True

Answer 5

You can directly obtain the edges in a cycle with the find_cycle method. If you want to test if an edge belongs to a cycle, you should check if both of its vertices are part of the same cycle.

Using the example in the answers above:

import networkx as nx

G = nx.Graph()
G.add_cycle([1,2,3,4])
G.add_cycle([10,20,30])
G.add_edge(1,10)
nx.find_cycle(G, 1) # [(1, 2), (2, 3), (3, 4), (4, 1)]
nx.find_cycle(G, 10) # [(10, 20), (20, 30), (30, 10)]

On the other hand, the edge (2, 3) (or (3, 2) as your graph is undirected) is part of a cycle defined first:

nx.find_cycle(G, 2) # [(2, 1), (1, 4), (4, 3), (3, 2)]