python: detecting a cycle in networkX

Question

As the title implies, I'm trying to write a function that will calculate the number of cycles any inputted node is part of. I found a helpful video which explains the theory behind an algorithm to find cycles, but I'm having trouble understanding how to implement it using networkX rather than the data structure that site is using. I couldn't understand the white/grey/etc set concept as well to traverse the network and find cycles.

My function parameters/structure:

def feedback_loop_counter(G, node):
    c = 0
    calculate all cycles in the network
    for every cycle node is in, increment c by 1
    return c

The network has input and output nodes too, and I'm unclear how those play into calculating cycles

This is my input network:

import networkx as nx
import matplotlib.pyplot as plt
G=nx.DiGraph()
molecules = ["CD40L", "CD40", "NF-kB", "XBP1", "Pax5", "Bach2", "Irf4", "IL-4", "IL-4R", "STAT6", "AID", "Blimp1", "Bcl6", "ERK", "BCR", "STAT3", "Ag", "STAT5", "IL-21R", "IL-21", "IL-2", "IL-2R"]
Bcl6 = [("Bcl6", "Bcl6"), ("Bcl6", "Blimp1"), ("Bcl6", "Irf4")]
STAT5 = [("STAT5", "Bcl6")]
IL_2R = [("IL-2R", "STAT5")]
IL_2 = [("IL-22", "IL-2R")]
BCR = [("BCR", "ERK")]
Ag = [("Ag", "BCR")]
CD40L = [("CD40L", "CD40")]
CD40 = [("CD40", "NF-B")]
NF_B = [("NF-B", "Irf4"), ("NF-B", "AID")]
Irf4 = [("Irf4", "Bcl6"), ("Irf4", "Pax5"), ("Irf4", "Irf4"), ("Irf4", "Blimp1")]
ERK = [("ERK", "Bcl6"), ("ERK", "Blimp1"), ("ERK", "Pax5")]
STAT3 = [("STAT3", "Blimp1")]
IL_21 = [("IL-21", "IL-21R")]
IL_21R = [("IL-21R", "STAT3")]
IL_4R = [("IL-4R", "STAT6")]
STAT6 = [("STAT6", "AID"), ("STAT6", "Bcl6")]
Bach2 = [("Bach2", "Blimp1")]
IL_4 = [("IL-4", "IL-4R")]
Blimp1 = [("Blimp1", "Bcl6"), ("Blimp1", "Bach2"), ("Blimp1", "Pax5"), ("Blimp1", "AID"), ("Blimp1", "Irf4")]
Pax5 = [("Pax5", "Pax5"), ("Pax5", "AID"), ("Pax5", "Bcl6"), ("Pax5", "Bach2"), ("Pax5", "XBP1"), ("Pax5", "ERK"), ("Pax5", "Blimp1")]
edges = Bcl6 + STAT5 + IL_2R + IL_2 + BCR + Ag + CD40L + CD40 + NF_B + Irf4 + 
ERK + STAT3 + IL_21 + IL_21R + IL_4R + STAT6 + Bach2 + IL_4 + Blimp1 + Pax5
G.add_nodes_from(molecules)
G.add_edges_from(edges)
sources = ["Ag", "CD40L", "IL-2", "IL-21", "IL-4"]
targets = ["XBP1", "AID"]

Answer 1

The idea to find cycles is to do a Depth-first search and while you do it, remember which nodes you already saw and the path to them. If you happen to visit a node you already saw, then there is a cycle, and you can find it by concatenating paths.

Try writing some code to do that, and open a new question with that code if you get stuck

Answer 2

I'm going to write my answer under the assumption you are interested in "simple cycles", that is, cycles whose only repeated node is the first/last node.

Take those nodes that have edges to a node u (the "input nodes"). Then use the networkx command all_simple_paths to find all simple paths from u to each of the input nodes. Each of these becomes a simple cycle.