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cliques.py

00001 """
Cliques   - Find and manipulate cliques of graphs

Note that finding the largest clique of a graph has been
shown to be an NP complete problem so the algorithms here
could take a LONG time to run.  In practice it hasn't been 
too bad for the graphs tested.
"""
__author__ = """Dan Schult (dschult@colgate.edu)"""
__date__ = "$Date: 2005-06-15 07:56:03 -0600 (Wed, 15 Jun 2005) $"
__credits__ = """"""
__revision__ = "$Revision: 1021 $"
#    Copyright (C) 2004,2005 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    Distributed under the terms of the GNU Lesser General Public License
#    http://www.gnu.org/copyleft/lesser.html

import networkx

00022 def find_cliques(G):
   """
   Find_cliques algorithm based on Bron & Kerbosch
   
   This algorithm searchs for maximal cliques in a graph.
   maximal cliques are the largest complete subgraph containing
   a given point.  The largest maximal clique is sometimes called
   the maximum clique.
   
   This algorithm produces the list of maximal cliques each
   of which are a list of the members of the clique.
   
   Based on Algol algorithm published by Bron & Kerbosch
   A C version is available as part of the rambin package.
   http://www.ram.org/computing/rambin/rambin.html

   Reference::

      @article{362367,
       author = {Coen Bron and Joep Kerbosch},
       title = {Algorithm 457: finding all cliques of an undirected graph},
       journal = {Commun. ACM},
       volume = {16},
       number = {9},
       year = {1973},
       issn = {0001-0782},
       pages = {575--577},
       doi = {http://doi.acm.org/10.1145/362342.362367},
       publisher = {ACM Press},
       }
   """
   all_nodes=G.nodes()
   num_nodes=G.order()
   clique=[]
   cliques=[]
   _extend(all_nodes,0,num_nodes,G,clique,cliques)
   return cliques

00060 def _extend(old_nodes,num_not,num_left,G,clique,cliques):
   """ 
   A recursive helper routine for find_cliques

   This recursive routine explores the "old_nodes" set of nodes
   for complete subgraphs.  num_left is the size of old_nodes. 
   The first num_not nodes are called the "not" group by B&K
   because they have already been considered. 
   The rest (num_left-num_not) of them are called "candidates".

   G is the graph, 
   clique is the clique being built,
   cliques is a list of maximal cliques found so far.
   """
   # set up sets nots and cands for easy reference
   cands=old_nodes[num_not:]
   nots=old_nodes[:num_not]

   #  Look for nodes that are "candidates" with the
   #  most neighbors among the "candidates"
   max_conn=0
   for p in cands:
      isneighbor=lambda v: G.has_edge(p,v)# "isneighbor" function
      conn=0       # count connections for ith node
      for nb in cands:   
        if isneighbor(nb):
           conn +=1
      if conn>max_conn:
         fixp=p
         max_conn=conn
         if max_conn > num_left-1: break  # found a most connected node
   
   # Note: if max_conn still zero, then no connections among candidates
   #     We can take a shortcut.
   #     If connects to a "not" node, we already got that clique
   #     Otherwise adding it makes a clique!
   if max_conn==0:
     for v in cands:
        not_conn=0
        isneighbor=lambda u:G.has_edge(v,u)  #"isneighbor" function
        for u in nots:
           if isneighbor(u):
              not_conn=1
              break
        if not_conn==0:
          clique.append(v)
##          print "New Maximal Clique Found!",clique
          cliques.append(clique[:])
          clique.remove(v)
     return

   # Set up the Best Candidate as our fixed point for this tree
   # best_position=old_nodes.index(fixp)
00113    fixpneighbor=lambda v: G.has_edge(fixp,v) #"isneighbor" function
   v=fixp

   # Go through each of the candidate 
   # nodes trying to build a clique
   #       cntr counts how many are left to check
   for cntr in range(num_left-num_not-max_conn,0,-1):
      # add the best node to the list of clique
##      print tt,"next candidate is:",v
      clique.append(v)
00123       isneighbor=lambda u: G.has_edge(v,u) # "isneighbor" function

      # Now create new lists to send to next recursion
      # fill new array--starting with "not" nodes
      new=[]
      for u in nots:
         if isneighbor(u):
            new.append(u)
      new_num_not=len(new)
      # now fill rest of new array with "candidate" nodes
      for u in cands:
         if isneighbor(u):
            new.append(u)
      new_num_left=len(new)

      # check if zero or one node left
      if new_num_left == 0:
         # Now there are no nodes left in "cand" or "not" to look at
         # we have found a maximal clique!!!
         cliques.append(clique[:])
##         print tt,"No nodes left so it must be a clique!"
##         print tt,"New Maximal Clique Found!",clique
      elif new_num_not<new_num_left:
         if new_num_left==1:
           #  Only one node left so it must be a clique!
           clique.append(new[0])
##           print tt,"Only one node left so it must be a clique!"
##           print tt,"New Maximal Clique Found!",clique
           cliques.append(clique[:])
           clique.remove(new[0])
         else:
           # Recursion on this routine
##            print tt,"Going into extend with cntr=",cntr
##            tt=tt + "  "
           _extend(new,new_num_not,new_num_left,G,clique,cliques)
##            tt=tt[0:len(tt)-2]  # go back to previous indentation 
##    else:    # new_num_not==new_num_left
##             # no new cliques so we're done with this candidate
##         print tt,"Only nodes from -not- left"


      # Done with checking branches for this node,
      # remove it from clique and add it to the NOT group
      clique.remove(v)
      nots.append(v)
      cands.remove(v)
      # find next candidate
00170       pos=0
      if cntr>1:
         while fixpneighbor(cands[pos]):
            pos += 1
         v=cands[pos]

00176 def make_max_clique_graph(G,create_using=None,**kwds):
    """ 
    Create the maximal clique graph of a graph.
    It finds the maximal cliques and treats these as nodes.
    The nodes are connected if they have common members in 
    the original graph.  Theory has done a lot with clique
    graphs, but I haven't seen much on maximal clique graphs.

    Note: This should be the same as make_clique_bipartite followed
    by project_up, but it saves all the intermediate stuff.
    """
    cliq=find_cliques(G)
    size=len(cliq)
    if create_using:
        B=create_using
    else:
        B=networkx.Graph(**kwds)

    for i in range(1,size+1):
        B.add_node(i)
        cl=cliq[i-1]
        for j in range(i+1,size+1):
            other_cl=cliq[j-1]
            intersect=[ w for w in cl if w in other_cl ]
            if intersect:     # Not empty list
                B.add_edge(i,j)
    return B

00204 def make_clique_bipartite(G,fpos=None,create_using=None,**kwds):
    """ 
    Create a bipartite clique graph from a graph G.
    Nodes of G are retained as the "bottom nodes" of B and 
    cliques of G become "top nodes" of B.
    Edges are present if a bottom node belongs to the clique 
    represented by the top node.
 
    Returns a Graph with additional attribute B.node_type
    which is "Bottom" or "Top" appropriately.

    if fpos is not None, a second additional attribute B.pos
    is created to hold the position tuple of each node for viewing
    the bipartite graph.
    """
    cliq=find_cliques(G)
    if create_using:
        B=create_using
    else:
        B=networkx.Graph(**kwds)
    B.add_nodes_from(G)
    B.node_type={}   # New Attribute for B
    for n in B:
        B.node_type[n]="Bottom"
 
    i=0
    if fpos is not None: 
       B.pos={}     # New Attribute for B
       delta_cpos=1./len(cliq)
       delta_ppos=1./G.order()
       cpos=0.
       ppos=0.
    for cl in cliq:
       i += 1
       name= -i   # Top nodes get negative names
       B.add_node(name)
       B.node_type[name]="Top"
       if fpos is not None: 
          if not B.pos.has_key(name):
             B.pos[name]=(0.2,cpos)
             cpos +=delta_cpos
       for v in cl:
          B.add_edge(name,v)
          if fpos is not None:
             if not B.pos.has_key(v):
                B.pos[v]=(0.8,ppos)
                ppos +=delta_ppos
    return B
   
00253 def project_down(B,create_using=None,**kwds):
    """ 
    Project a bipartite graph B down onto its "Bottom Nodes".
    The nodes retain their names and are connected if they
    share a common Top Node in the Bipartite Graph.
    Returns a Graph.
    """
    if create_using:
        G=create_using
    else:
        G=networkx.Graph(**kwds)
    for v in B.nodes():
       if B.node_type[v]=="Bottom":
          G.add_node(v)
          for cv in B.neighbors(v):
             G.add_edges_from([(v,u) for u in B.neighbors(cv)])
    return G
 
00271 def project_up(B,create_using=None,**kwds):
    """ 
    Project a bipartite graph B up onto its "Top Nodes".
    The nodes retain their names and are connected if they
    share a common Bottom Node in the Bipartite Graph.
    Returns a Graph.
    """
    if create_using:
        G=create_using
    else:
        G=networkx.Graph(**kwds)
    for v in B.nodes():
       if B.node_type[v]=="Top":
          vname= -v   #Change sign of name for Top Nodes
          G.add_node(vname)
          for cv in B.neighbors(v):
             # Note: -u changes the name (not Top node anymore)
             G.add_edges_from([(vname,-u) for u in B.neighbors(cv) if u!=v])
    return G
 
00291 def graph_clique_number(G,cliques=None):
    """Return the clique number (size the largest clique) for G.
       Optional list of cliques can be input if already computed.
    """
    if cliques is None:
        cliques=find_cliques(G)
    return   max( [len(c) for c in cliques] )


00300 def graph_number_of_cliques(G,cliques=None):
    """  Returns the number of maximal cliques in G
       Optional list of cliques can be input if already computed.
    """
    if cliques is None:
        cliques=find_cliques(G)
    return   len(cliques)

 
00309 def node_clique_number(G,nodes=None,with_labels=False,cliques=None):
    """ Returns the size of the largest maximal clique containing
        each given node.  

        Returns a single or list depending on input nodes.
        Returns a dict keyed by node if "with_labels=True".
        Optional list of cliques can be input if already computed.
    """
    if nodes is None:                 # none, use entire graph
        nodes=G.nodes()
    elif  not isinstance(nodes, list):    # check for a list
        nodes=[nodes]             # assume it is a single value

    if cliques is None:
        cliques=find_cliques(G)
    d={}
    for v in nodes:
        d[v]=max([len(c) for c in cliques if v in c])
    
    if with_labels: return d
    if len(d)==1: return d[v] #return single value
    return d.values()


00333 def number_of_cliques(G,nodes=None,cliques=None,with_labels=False):
    """ Returns the number of maximal cliques for each node.

        Returns a single or list depending on input nodes.
        Returns a dict keyed by node if "with_labels=True".
        Optional list of cliques can be input if already computed.
    """
    if nodes is None:
        nodes=G.nodes()   # none, get entire graph
    elif  not isinstance(nodes, list):    # check for a list
        nodes=[nodes]             # assume it is a single value

    if cliques is None:
        cliques=find_cliques(G)
    numcliq={}
    for v in nodes:
        numcliq[v]=len([1 for c in cliques if v in c])

    if with_labels: return numcliq
    if len(numcliq)==1: return numcliq[v]
    return numcliq.values()
    
00355 def cliques_containing_node(G,nodes=None,cliques=None,with_labels=False):
    """ Returns a list of cliques containing the given node.

        Returns a single list or list of lists depending on input nodes.
        Returns a dict keyed by node if "with_labels=True".
        Optional list of cliques can be input if already computed.
    """
    if nodes is None:
        nodes=G.nodes()   # none, get entire graph
    elif  not isinstance(nodes, list):    # check for a list
        nodes=[nodes]             # assume it is a single value

    if cliques is None:
        cliques=find_cliques(G)
    vcliques={}
    for v in nodes:
        vcliques[v]=[c for c in cliques if v in c]

    if with_labels: return vcliques
    if len(vcliques)==1: return vcliques[v]
    return vcliques.values()

def _test_suite():
    import doctest
    suite = doctest.DocFileSuite('tests/cliques.txt',package='networkx')
    return suite


if __name__ == "__main__":
    import os   
    import sys
    import unittest
    if sys.version_info[:2] < (2, 4):
        print "Python version 2.4 or later required for tests (%d.%d detected)." %  sys.version_info[:2]
        sys.exit(-1)
    # directory of networkx package (relative to this)
    nxbase=sys.path[0]+os.sep+os.pardir
    sys.path.insert(0,nxbase) # prepend to search path
    unittest.TextTestRunner().run(_test_suite())
    

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