Re: [igraph] Community finding in graphs

[Tamas Nepusz]

Hi,

>    I just found an intriguing community detection algorithm that  
> tries to
> reflect overlaps
A quick implementation in Python (and I assume it's similar in R):

# g is an undirected graph. If not, keep only the mutual edge pairs  
before doing this
from igraph import *

# search for all cliques
cliques = [set(clique) for clique in g.cliques(min=3)]

# sort the cliques by length
cliques_by_length = {}
for clique in cliques:
  k = len(clique)
  if not cliques_by_length.has_key(k): cliques_by_length[k] = []
  cliques_by_length[k].append(clique)

for k in cliques_by_length.keys():
  # create clique adjacency graph for all k
  adjacencies = []
  cs = cliques_by_length[k]
  for idx1, c1 in enumerate(cs):
    for idx2, c2 in enumerate(cs):
      if len(c1.union(c2)) == k+1:
        adjacencies.append((idx1, idx2))
  clique_graph = Graph(len(cs), adjacencies)
  # determine the connected components
  components = clique_graph.components()

  print "k=%d:" % k
  for component in components:
    community = set()
    for clique_idx in component: community.update(cs[clique_idx])
    print "  %s" % str(community)

This should work for small and medium sized sparse graphs. Note that  
the clique detection routine in igraph uses substantially less memory  
in the dev tree than in the last stable version, so you might consider  
installing the development version.

--
T.