Internal Link Detection on Bipartite Graph

internal_links.py

# -*- coding: utf-8 -*-
#!/usr/bin/env python
"""
==========================================
Internal Link Detection on Bipartite Graph
==========================================
#	Copyright (C) 2012 by
#	Sébastien Heymann <[email protected]>
#	All rights reserved.
#	BSD license.

Detect internal links in a bipartite graph, using the top set of nodes.
An internal link is a link in the bipartite graph which does not change 
the projection of the graph onto the top set of nodes if it is removed.

References
----------
O. Allali, L. Tabourier, C. Magnien, M. Latapy,
"Internal links and pairs as a new tool for the analysis of bipartite complex networks",
To appear in Social Network Analysis and Mining, 2012.
http://www.complexnetworks.fr/wp-content/uploads/2012/01/Allali_internal_links.pdf

Input
-----
List of links (may be compressed in GZIP).
One link (top node, bottom node) per line with extremities separated by a space.
Each node should have a unique string identifier and may be delimited by double quotes.
The file should NOT contain comment lines (e.g. starting with '#').
Example:
u0 v0
u0 v2
u0 v3
u1 v1
u1 v3
u2 v2
u2 v1
u2 v4
u2 v0
u2 v3
u3 v2
u3 v4

Output
------
List of internal links. 

Requires
--------
Python 2.7
Networkx 1.7+.

Usage
-------
python2.7 get_internal_links.py my_edgelist.gz internal_links.edgelist
"""

def read_edge_list(filepath):
	"""Read an edgelist file in plain text of GZIP compressed format."""
	try:
		import csv
		import gzip
	except ImportError:
		raise ImportError('get_internal_links() requires csv and gzip')
	try:
		f = gzip.GzipFile(filepath, 'rb').read(1)  #raise exception if not a GZ
		f = gzip.open(filepath, 'rb')
	except IOError:
		f = open(filepath, 'r')
	reader = csv.reader(f, delimiter=' ', quotechar='"')
	edgelist = [(row[0], row[1]) for row in reader if row]  # (top node, bottom node)
	return edgelist

def get_internal_links(B, nodes):
	"""Return the set of internal links of the bipartite graph B, 
	projected onto one of its node sets.

	Parameters
	----------
	B : NetworkX graph
	nodes : 

	Returns
	-------
	I : set
	  A set of tuples (u,v) which are the internal links detected.

	Raises
	------
	AssertionError if the graph is not bipartite.

	Examples
	--------
	B = nx.Graph()
	B.add_nodes_from([1,2,3,4], bipartite=0)
	B.add_nodes_from(['a','b','c'], bipartite=1)
	B.add_edges_from([(1,'a'), (1,'b'), (2,'b'), (2,'c'), (3,'c'), (4,'a')])
	bottomNodes, topNodes = bipartite.sets(B)
	print(get_internal_links(B, topNodes))
	"""
	try:
		from collections import Counter
	except ImportError:
		raise ImportError('get_internal_links() requires collections.Counter ')
	try:
		import itertools
	except ImportError:
		raise ImportError('get_internal_links() requires itertools ')
	try:
		import networkx as nx
		from networkx.algorithms import bipartite
	except ImportError:
		raise ImportError('get_internal_links() requires networkx ')
	assert bipartite.is_bipartite(B)
	I = set()
	for u in nodes:
		m = set(B[u])
		cnt = Counter()
		Nv = (w for v in m for w in B[v])  # iterator on w in B[v], for each v in m
		for w in Nv:
			cnt[w] += 1
		cnt[u] = 0
		r = set(itertools.chain(*[B[w] for w, times in cnt.iteritems() if times == 1]))
		m -= r
		I.update((u,v) for v in m)
	return I

	# NAIVE IMPLEMENTATION:
	# I = set()
	# for u in nodes:
	# 	d = {}
	# 	m = B[u]
	# 	for v in m:
	# 		Nv = B[v]
	# 		for w in Nv:
	# 			d[w] = d[w] + 1 if w in d else 1
	#	d[u] = 0
	# 	r = itertools.chain(*[B[w] for w, times in d.iteritems() if times == 1])
	# 	Iu = set((u,v) for v in m if v not in r)
	# 	I |= Iu


if __name__ == "__main__":
	import argparse
	import networkx as nx

	#read command line arguments
	parser = argparse.ArgumentParser()
	parser.add_argument("inputFile", help="Path to the input file.")
	parser.add_argument("outputFile", help="Path to the output file.")
	parser.add_argument("-r", "--reverse", 
		help="Use the bottom set of nodes to detect the internal links.", 
		action="store_true")
	parser.add_argument("-q", "--quiet", 
		help="No information on the standard output but critical errors.", 
		action="store_true")
	args = parser.parse_args()

	#load the bipartite graph
	if not args.quiet:
		print 'load graph'
	G = nx.Graph()
	links = read_edge_list(args.inputFile)

	for (u,v) in links:
		G.add_node(u, bipartite=0)  #top node
		G.add_node(v, bipartite=1)  #bottom node
		G.add_edge(u, v)

	topNodes = set(n for n,d in G.nodes(data=True) if d['bipartite']==0)
	bottomNodes = set(G) - topNodes

	if not args.quiet:
		print "nb top nodes: ", len(topNodes)
		print "nb bottom nodes: ", len(bottomNodes)
		print "nb links: ", G.number_of_edges()
		print 'detect internal links'

	#detect internal links
	nodes = bottomNodes if args.reverse else topNodes
	I = get_internal_links(G, nodes)

	if not args.quiet:
		print 'nb internal links: ', len(I)
		print 'write output file'

	#write output file
	f = open(args.outputFile, 'w')
	for (u, v) in I:
		#assert G.has_edge(u,v), 'link not in graph'
		f.write(str(u)+' '+str(v)+'\n')  # top bottom
	f.close()