# -*- coding: utf-8 -*-
"""
Generators and functions for bipartite graphs.
"""
# Copyright (C) 2006-2011 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import math
import random
import networkx
from functools import reduce
import networkx as nx
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
__all__=['bipartite_configuration_model',
'bipartite_havel_hakimi_graph',
'bipartite_reverse_havel_hakimi_graph',
'bipartite_alternating_havel_hakimi_graph',
'bipartite_preferential_attachment_graph',
'bipartite_random_graph',
'bipartite_gnmk_random_graph',
]
[docs]def bipartite_configuration_model(aseq, bseq, create_using=None, seed=None):
"""Return a random bipartite graph from two given degree sequences.
Parameters
----------
aseq : list or iterator
Degree sequence for node set A.
bseq : list or iterator
Degree sequence for node set B.
create_using : NetworkX graph instance, optional
Return graph of this type.
seed : integer, optional
Seed for random number generator.
Nodes from the set A are connected to nodes in the set B by
choosing randomly from the possible free stubs, one in A and
one in B.
Notes
-----
The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
If no graph type is specified use MultiGraph with parallel edges.
If you want a graph with no parallel edges use create_using=Graph()
but then the resulting degree sequences might not be exact.
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
to indicate which bipartite set the node belongs to.
"""
if create_using is None:
create_using=networkx.MultiGraph()
elif create_using.is_directed():
raise networkx.NetworkXError(\
"Directed Graph not supported")
G=networkx.empty_graph(0,create_using)
if not seed is None:
random.seed(seed)
# length and sum of each sequence
lena=len(aseq)
lenb=len(bseq)
suma=sum(aseq)
sumb=sum(bseq)
if not suma==sumb:
raise networkx.NetworkXError(\
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'\
%(suma,sumb))
G=_add_nodes_with_bipartite_label(G,lena,lenb)
if max(aseq)==0: return G # done if no edges
# build lists of degree-repeated vertex numbers
stubs=[]
stubs.extend([[v]*aseq[v] for v in range(0,lena)])
astubs=[]
astubs=[x for subseq in stubs for x in subseq]
stubs=[]
stubs.extend([[v]*bseq[v-lena] for v in range(lena,lena+lenb)])
bstubs=[]
bstubs=[x for subseq in stubs for x in subseq]
# shuffle lists
random.shuffle(astubs)
random.shuffle(bstubs)
G.add_edges_from([[astubs[i],bstubs[i]] for i in range(suma)])
G.name="bipartite_configuration_model"
return G
[docs]def bipartite_havel_hakimi_graph(aseq, bseq, create_using=None):
"""Return a bipartite graph from two given degree sequences using a
Havel-Hakimi style construction.
Nodes from the set A are connected to nodes in the set B by
connecting the highest degree nodes in set A to the highest degree
nodes in set B until all stubs are connected.
Parameters
----------
aseq : list or iterator
Degree sequence for node set A.
bseq : list or iterator
Degree sequence for node set B.
create_using : NetworkX graph instance, optional
Return graph of this type.
Notes
-----
The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
If no graph type is specified use MultiGraph with parallel edges.
If you want a graph with no parallel edges use create_using=Graph()
but then the resulting degree sequences might not be exact.
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
to indicate which bipartite set the node belongs to.
"""
if create_using is None:
create_using=networkx.MultiGraph()
elif create_using.is_directed():
raise networkx.NetworkXError(\
"Directed Graph not supported")
G=networkx.empty_graph(0,create_using)
# length of the each sequence
naseq=len(aseq)
nbseq=len(bseq)
suma=sum(aseq)
sumb=sum(bseq)
if not suma==sumb:
raise networkx.NetworkXError(\
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'\
%(suma,sumb))
G=_add_nodes_with_bipartite_label(G,naseq,nbseq)
if max(aseq)==0: return G # done if no edges
# build list of degree-repeated vertex numbers
astubs=[[aseq[v],v] for v in range(0,naseq)]
bstubs=[[bseq[v-naseq],v] for v in range(naseq,naseq+nbseq)]
astubs.sort()
while astubs:
(degree,u)=astubs.pop() # take of largest degree node in the a set
if degree==0: break # done, all are zero
# connect the source to largest degree nodes in the b set
bstubs.sort()
for target in bstubs[-degree:]:
v=target[1]
G.add_edge(u,v)
target[0] -= 1 # note this updates bstubs too.
if target[0]==0:
bstubs.remove(target)
G.name="bipartite_havel_hakimi_graph"
return G
[docs]def bipartite_reverse_havel_hakimi_graph(aseq, bseq, create_using=None):
"""Return a bipartite graph from two given degree sequences using a
Havel-Hakimi style construction.
Nodes from set A are connected to nodes in the set B by connecting
the highest degree nodes in set A to the lowest degree nodes in
set B until all stubs are connected.
Parameters
----------
aseq : list or iterator
Degree sequence for node set A.
bseq : list or iterator
Degree sequence for node set B.
create_using : NetworkX graph instance, optional
Return graph of this type.
Notes
-----
The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
If no graph type is specified use MultiGraph with parallel edges.
If you want a graph with no parallel edges use create_using=Graph()
but then the resulting degree sequences might not be exact.
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
to indicate which bipartite set the node belongs to.
"""
if create_using is None:
create_using=networkx.MultiGraph()
elif create_using.is_directed():
raise networkx.NetworkXError(\
"Directed Graph not supported")
G=networkx.empty_graph(0,create_using)
# length of the each sequence
lena=len(aseq)
lenb=len(bseq)
suma=sum(aseq)
sumb=sum(bseq)
if not suma==sumb:
raise networkx.NetworkXError(\
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'\
%(suma,sumb))
G=_add_nodes_with_bipartite_label(G,lena,lenb)
if max(aseq)==0: return G # done if no edges
# build list of degree-repeated vertex numbers
astubs=[[aseq[v],v] for v in range(0,lena)]
bstubs=[[bseq[v-lena],v] for v in range(lena,lena+lenb)]
astubs.sort()
bstubs.sort()
while astubs:
(degree,u)=astubs.pop() # take of largest degree node in the a set
if degree==0: break # done, all are zero
# connect the source to the smallest degree nodes in the b set
for target in bstubs[0:degree]:
v=target[1]
G.add_edge(u,v)
target[0] -= 1 # note this updates bstubs too.
if target[0]==0:
bstubs.remove(target)
G.name="bipartite_reverse_havel_hakimi_graph"
return G
[docs]def bipartite_alternating_havel_hakimi_graph(aseq, bseq,create_using=None):
"""Return a bipartite graph from two given degree sequences using
an alternating Havel-Hakimi style construction.
Nodes from the set A are connected to nodes in the set B by
connecting the highest degree nodes in set A to alternatively the
highest and the lowest degree nodes in set B until all stubs are
connected.
Parameters
----------
aseq : list or iterator
Degree sequence for node set A.
bseq : list or iterator
Degree sequence for node set B.
create_using : NetworkX graph instance, optional
Return graph of this type.
Notes
-----
The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
If no graph type is specified use MultiGraph with parallel edges.
If you want a graph with no parallel edges use create_using=Graph()
but then the resulting degree sequences might not be exact.
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
to indicate which bipartite set the node belongs to.
"""
if create_using is None:
create_using=networkx.MultiGraph()
elif create_using.is_directed():
raise networkx.NetworkXError(\
"Directed Graph not supported")
G=networkx.empty_graph(0,create_using)
# length of the each sequence
naseq=len(aseq)
nbseq=len(bseq)
suma=sum(aseq)
sumb=sum(bseq)
if not suma==sumb:
raise networkx.NetworkXError(\
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'\
%(suma,sumb))
G=_add_nodes_with_bipartite_label(G,naseq,nbseq)
if max(aseq)==0: return G # done if no edges
# build list of degree-repeated vertex numbers
astubs=[[aseq[v],v] for v in range(0,naseq)]
bstubs=[[bseq[v-naseq],v] for v in range(naseq,naseq+nbseq)]
while astubs:
astubs.sort()
(degree,u)=astubs.pop() # take of largest degree node in the a set
if degree==0: break # done, all are zero
bstubs.sort()
small=bstubs[0:degree // 2] # add these low degree targets
large=bstubs[(-degree+degree // 2):] # and these high degree targets
stubs=[x for z in zip(large,small) for x in z] # combine, sorry
if len(stubs)<len(small)+len(large): # check for zip truncation
stubs.append(large.pop())
for target in stubs:
v=target[1]
G.add_edge(u,v)
target[0] -= 1 # note this updates bstubs too.
if target[0]==0:
bstubs.remove(target)
G.name="bipartite_alternating_havel_hakimi_graph"
return G
[docs]def bipartite_preferential_attachment_graph(aseq,p,create_using=None,seed=None):
"""Create a bipartite graph with a preferential attachment model from
a given single degree sequence.
Parameters
----------
aseq : list or iterator
Degree sequence for node set A.
p : float
Probability that a new bottom node is added.
create_using : NetworkX graph instance, optional
Return graph of this type.
seed : integer, optional
Seed for random number generator.
References
----------
.. [1] Jean-Loup Guillaume and Matthieu Latapy,
Bipartite structure of all complex networks,
Inf. Process. Lett. 90, 2004, pg. 215-221
http://dx.doi.org/10.1016/j.ipl.2004.03.007
"""
if create_using is None:
create_using=networkx.MultiGraph()
elif create_using.is_directed():
raise networkx.NetworkXError(\
"Directed Graph not supported")
if p > 1:
raise networkx.NetworkXError("probability %s > 1"%(p))
G=networkx.empty_graph(0,create_using)
if not seed is None:
random.seed(seed)
naseq=len(aseq)
G=_add_nodes_with_bipartite_label(G,naseq,0)
vv=[ [v]*aseq[v] for v in range(0,naseq)]
while vv:
while vv[0]:
source=vv[0][0]
vv[0].remove(source)
if random.random() < p or G.number_of_nodes() == naseq:
target=G.number_of_nodes()
G.add_node(target,bipartite=1)
G.add_edge(source,target)
else:
bb=[ [b]*G.degree(b) for b in range(naseq,G.number_of_nodes())]
# flatten the list of lists into a list.
bbstubs=reduce(lambda x,y: x+y, bb)
# choose preferentially a bottom node.
target=random.choice(bbstubs)
G.add_node(target,bipartite=1)
G.add_edge(source,target)
vv.remove(vv[0])
G.name="bipartite_preferential_attachment_model"
return G
[docs]def bipartite_random_graph(n, m, p, seed=None, directed=False):
"""Return a bipartite random graph.
This is a bipartite version of the binomial (Erdős-Rényi) graph.
Parameters
----------
n : int
The number of nodes in the first bipartite set.
m : int
The number of nodes in the second bipartite set.
p : float
Probability for edge creation.
seed : int, optional
Seed for random number generator (default=None).
directed : bool, optional (default=False)
If True return a directed graph
Notes
-----
The bipartite random graph algorithm chooses each of the n*m (undirected)
or 2*nm (directed) possible edges with probability p.
This algorithm is O(n+m) where m is the expected number of edges.
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
to indicate which bipartite set the node belongs to.
See Also
--------
gnp_random_graph, bipartite_configuration_model
References
----------
.. [1] Vladimir Batagelj and Ulrik Brandes,
"Efficient generation of large random networks",
Phys. Rev. E, 71, 036113, 2005.
"""
G=nx.Graph()
G=_add_nodes_with_bipartite_label(G,n,m)
if directed:
G=nx.DiGraph(G)
G.name="fast_gnp_random_graph(%s,%s,%s)"%(n,m,p)
if not seed is None:
random.seed(seed)
if p <= 0:
return G
if p >= 1:
return nx.complete_bipartite_graph(n,m)
lp = math.log(1.0 - p)
v = 0
w = -1
while v < n:
lr = math.log(1.0 - random.random())
w = w + 1 + int(lr/lp)
while w >= m and v < n:
w = w - m
v = v + 1
if v < n:
G.add_edge(v, n+w)
if directed:
# use the same algorithm to
# add edges from the "m" to "n" set
v = 0
w = -1
while v < n:
lr = math.log(1.0 - random.random())
w = w + 1 + int(lr/lp)
while w>= m and v < n:
w = w - m
v = v + 1
if v < n:
G.add_edge(n+w, v)
return G
[docs]def bipartite_gnmk_random_graph(n, m, k, seed=None, directed=False):
"""Return a random bipartite graph G_{n,m,k}.
Produces a bipartite graph chosen randomly out of the set of all graphs
with n top nodes, m bottom nodes, and k edges.
Parameters
----------
n : int
The number of nodes in the first bipartite set.
m : int
The number of nodes in the second bipartite set.
k : int
The number of edges
seed : int, optional
Seed for random number generator (default=None).
directed : bool, optional (default=False)
If True return a directed graph
Examples
--------
G = nx.bipartite_gnmk_random_graph(10,20,50)
See Also
--------
gnm_random_graph
Notes
-----
If k > m * n then a complete bipartite graph is returned.
This graph is a bipartite version of the `G_{nm}` random graph model.
"""
G = networkx.Graph()
G=_add_nodes_with_bipartite_label(G,n,m)
if directed:
G=nx.DiGraph(G)
G.name="bipartite_gnm_random_graph(%s,%s,%s)"%(n,m,k)
if seed is not None:
random.seed(seed)
if n == 1 or m == 1:
return G
max_edges = n*m # max_edges for bipartite networks
if k >= max_edges: # Maybe we should raise an exception here
return networkx.complete_bipartite_graph(n, m, create_using=G)
top = [n for n,d in G.nodes(data=True) if d['bipartite']==0]
bottom = list(set(G) - set(top))
edge_count = 0
while edge_count < k:
# generate random edge,u,v
u = random.choice(top)
v = random.choice(bottom)
if v in G[u]:
continue
else:
G.add_edge(u,v)
edge_count += 1
return G
def _add_nodes_with_bipartite_label(G, lena, lenb):
G.add_nodes_from(range(0,lena+lenb))
b=dict(zip(range(0,lena),[0]*lena))
b.update(dict(zip(range(lena,lena+lenb),[1]*lenb)))
nx.set_node_attributes(G,'bipartite',b)
return G