Finding cycle of 3 nodes ( or triangles) in a graph

Question

I am working with complex networks. I want to find group of nodes which forms a cycle of 3 nodes (or triangles) in a given graph. As my graph contains about million edges, u

Answer 1

A million edges is quite small. Unless you are doing it thousands of times, just use a naive implementation.

I'll assume that you have a dictionary of node_ids, which point to a sequence of their neighbors, and that the graph is directed.

For example:

nodes = {}
nodes[0] = 1,2
nodes[1] = tuple() # empty tuple
nodes[2] = 1

My solution:

def generate_triangles(nodes):
    """Generate triangles. Weed out duplicates."""
    visited_ids = set() # remember the nodes that we have tested already
    for node_a_id in nodes:
        for node_b_id in nodes[node_a_id]:
            if nod_b_id == node_a_id:
                raise ValueError # nodes shouldn't point to themselves
            if node_b_id in visited_ids:
                continue # we should have already found b->a->??->b
            for node_c_id in nodes[node_b_id]:
                if node_c_id in visited_ids:
                    continue # we should have already found c->a->b->c
                if node_a_id in nodes[node_c_id]:
                    yield(node_a_id, node_b_id, node_c_id)
        visited_ids.add(node_a_id) # don't search a - we already have all those cycles

Checking performance:

from random import randint
n = 1000000
node_list = range(n)
nodes = {}
for node_id in node_list:
    node = tuple()
    for i in range(randint(0,10)): # add up to 10 neighbors
        try:
            neighbor_id = node_list[node_id+randint(-5,5)] # pick a nearby node
        except:
            continue 
        if not neighbor_id in node:
            node = node + (neighbor_id,)
    nodes[node_id] = node

cycles = list(generate_triangles(nodes))
print len(cycles)

When I tried it, it took longer to build the random graph than to count the cycles.

You might want to test it though ;) I won't guarantee that it's correct.

You could also look into networkx, which is the big python graph library.