607 lines
20 KiB
Python
607 lines
20 KiB
Python
|
# -*- coding: utf-8 -*-
|
||
|
|
# 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.
|
||
|
|
#
|
||
|
|
# Authors: Aric Hagberg <aric.hagberg@gmail.com>
|
||
|
|
# Pieter Swart <swart@lanl.gov>
|
||
|
|
# Dan Schult <dschult@colgate.edu>
|
||
|
|
"""
|
||
|
|
Generators and functions for bipartite graphs.
|
||
|
|
"""
|
||
|
|
import math
|
||
|
|
import numbers
|
||
|
|
import random
|
||
|
|
from functools import reduce
|
||
|
|
import networkx as nx
|
||
|
|
from networkx.utils import nodes_or_number, py_random_state
|
||
|
|
|
||
|
|
__all__ = ['configuration_model',
|
||
|
|
'havel_hakimi_graph',
|
||
|
|
'reverse_havel_hakimi_graph',
|
||
|
|
'alternating_havel_hakimi_graph',
|
||
|
|
'preferential_attachment_graph',
|
||
|
|
'random_graph',
|
||
|
|
'gnmk_random_graph',
|
||
|
|
'complete_bipartite_graph',
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
@nodes_or_number([0, 1])
|
||
|
|
def complete_bipartite_graph(n1, n2, create_using=None):
|
||
|
|
"""Returns the complete bipartite graph `K_{n_1,n_2}`.
|
||
|
|
|
||
|
|
The graph is composed of two partitions with nodes 0 to (n1 - 1)
|
||
|
|
in the first and nodes n1 to (n1 + n2 - 1) in the second.
|
||
|
|
Each node in the first is connected to each node in the second.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
n1 : integer
|
||
|
|
Number of nodes for node set A.
|
||
|
|
n2 : integer
|
||
|
|
Number of nodes for node set B.
|
||
|
|
create_using : NetworkX graph instance, optional
|
||
|
|
Return graph of this type.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Node labels are the integers 0 to `n_1 + n_2 - 1`.
|
||
|
|
|
||
|
|
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
|
||
|
|
to indicate which bipartite set the node belongs to.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.complete_bipartite_graph
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
n1, top = n1
|
||
|
|
n2, bottom = n2
|
||
|
|
if isinstance(n2, numbers.Integral):
|
||
|
|
bottom = [n1 + i for i in bottom]
|
||
|
|
G.add_nodes_from(top, bipartite=0)
|
||
|
|
G.add_nodes_from(bottom, bipartite=1)
|
||
|
|
G.add_edges_from((u, v) for u in top for v in bottom)
|
||
|
|
G.graph['name'] = "complete_bipartite_graph(%s,%s)" % (n1, n2)
|
||
|
|
return G
|
||
|
|
|
||
|
|
|
||
|
|
@py_random_state(3)
|
||
|
|
def configuration_model(aseq, bseq, create_using=None, seed=None):
|
||
|
|
"""Returns a random bipartite graph from two given degree sequences.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
aseq : list
|
||
|
|
Degree sequence for node set A.
|
||
|
|
bseq : list
|
||
|
|
Degree sequence for node set B.
|
||
|
|
create_using : NetworkX graph instance, optional
|
||
|
|
Return graph of this type.
|
||
|
|
seed : integer, random_state, or None (default)
|
||
|
|
Indicator of random number generation state.
|
||
|
|
See :ref:`Randomness<randomness>`.
|
||
|
|
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
|
||
|
|
Nodes from set A are connected to nodes in 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.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.configuration_model
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
# length and sum of each sequence
|
||
|
|
lena = len(aseq)
|
||
|
|
lenb = len(bseq)
|
||
|
|
suma = sum(aseq)
|
||
|
|
sumb = sum(bseq)
|
||
|
|
|
||
|
|
if not suma == sumb:
|
||
|
|
raise nx.NetworkXError(
|
||
|
|
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'
|
||
|
|
% (suma, sumb))
|
||
|
|
|
||
|
|
G = _add_nodes_with_bipartite_label(G, lena, lenb)
|
||
|
|
|
||
|
|
if len(aseq) == 0 or 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
|
||
|
|
seed.shuffle(astubs)
|
||
|
|
seed.shuffle(bstubs)
|
||
|
|
|
||
|
|
G.add_edges_from([[astubs[i], bstubs[i]] for i in range(suma)])
|
||
|
|
|
||
|
|
G.name = "bipartite_configuration_model"
|
||
|
|
return G
|
||
|
|
|
||
|
|
|
||
|
|
def havel_hakimi_graph(aseq, bseq, create_using=None):
|
||
|
|
"""Returns a bipartite graph from two given degree sequences using a
|
||
|
|
Havel-Hakimi style construction.
|
||
|
|
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
|
||
|
|
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
|
||
|
|
Degree sequence for node set A.
|
||
|
|
bseq : list
|
||
|
|
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.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.havel_hakimi_graph
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
# length of the each sequence
|
||
|
|
naseq = len(aseq)
|
||
|
|
nbseq = len(bseq)
|
||
|
|
|
||
|
|
suma = sum(aseq)
|
||
|
|
sumb = sum(bseq)
|
||
|
|
|
||
|
|
if not suma == sumb:
|
||
|
|
raise nx.NetworkXError(
|
||
|
|
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'
|
||
|
|
% (suma, sumb))
|
||
|
|
|
||
|
|
G = _add_nodes_with_bipartite_label(G, naseq, nbseq)
|
||
|
|
|
||
|
|
if len(aseq) == 0 or 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
|
||
|
|
|
||
|
|
|
||
|
|
def reverse_havel_hakimi_graph(aseq, bseq, create_using=None):
|
||
|
|
"""Returns a bipartite graph from two given degree sequences using a
|
||
|
|
Havel-Hakimi style construction.
|
||
|
|
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
|
||
|
|
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
|
||
|
|
Degree sequence for node set A.
|
||
|
|
bseq : list
|
||
|
|
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.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.reverse_havel_hakimi_graph
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
# length of the each sequence
|
||
|
|
lena = len(aseq)
|
||
|
|
lenb = len(bseq)
|
||
|
|
suma = sum(aseq)
|
||
|
|
sumb = sum(bseq)
|
||
|
|
|
||
|
|
if not suma == sumb:
|
||
|
|
raise nx.NetworkXError(
|
||
|
|
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'
|
||
|
|
% (suma, sumb))
|
||
|
|
|
||
|
|
G = _add_nodes_with_bipartite_label(G, lena, lenb)
|
||
|
|
|
||
|
|
if len(aseq) == 0 or 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
|
||
|
|
|
||
|
|
|
||
|
|
def alternating_havel_hakimi_graph(aseq, bseq, create_using=None):
|
||
|
|
"""Returns a bipartite graph from two given degree sequences using
|
||
|
|
an alternating Havel-Hakimi style construction.
|
||
|
|
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
|
||
|
|
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
|
||
|
|
Degree sequence for node set A.
|
||
|
|
bseq : list
|
||
|
|
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.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.alternating_havel_hakimi_graph
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
# length of the each sequence
|
||
|
|
naseq = len(aseq)
|
||
|
|
nbseq = len(bseq)
|
||
|
|
suma = sum(aseq)
|
||
|
|
sumb = sum(bseq)
|
||
|
|
|
||
|
|
if not suma == sumb:
|
||
|
|
raise nx.NetworkXError(
|
||
|
|
'invalid degree sequences, sum(aseq)!=sum(bseq),%s,%s'
|
||
|
|
% (suma, sumb))
|
||
|
|
|
||
|
|
G = _add_nodes_with_bipartite_label(G, naseq, nbseq)
|
||
|
|
|
||
|
|
if len(aseq) == 0 or 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):] # now 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
|
||
|
|
|
||
|
|
|
||
|
|
@py_random_state(3)
|
||
|
|
def 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.
|
||
|
|
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(len(aseq) - 1) and set B has nodes starting with node len(aseq).
|
||
|
|
The number of nodes in set B is random.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
aseq : list
|
||
|
|
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, random_state, or None (default)
|
||
|
|
Indicator of random number generation state.
|
||
|
|
See :ref:`Randomness<randomness>`.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] Guillaume, J.L. and Latapy, M.,
|
||
|
|
Bipartite graphs as models of complex networks.
|
||
|
|
Physica A: Statistical Mechanics and its Applications,
|
||
|
|
2006, 371(2), pp.795-813.
|
||
|
|
.. [2] Jean-Loup Guillaume and Matthieu Latapy,
|
||
|
|
Bipartite structure of all complex networks,
|
||
|
|
Inf. Process. Lett. 90, 2004, pg. 215-221
|
||
|
|
https://doi.org/10.1016/j.ipl.2004.03.007
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
|
||
|
|
to indicate which bipartite set the node belongs to.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.preferential_attachment_graph
|
||
|
|
"""
|
||
|
|
G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
|
||
|
|
if G.is_directed():
|
||
|
|
raise nx.NetworkXError("Directed Graph not supported")
|
||
|
|
|
||
|
|
if p > 1:
|
||
|
|
raise nx.NetworkXError("probability %s > 1" % (p))
|
||
|
|
|
||
|
|
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 seed.random() < p or len(G) == naseq:
|
||
|
|
target = len(G)
|
||
|
|
G.add_node(target, bipartite=1)
|
||
|
|
G.add_edge(source, target)
|
||
|
|
else:
|
||
|
|
bb = [[b] * G.degree(b) for b in range(naseq, len(G))]
|
||
|
|
# flatten the list of lists into a list.
|
||
|
|
bbstubs = reduce(lambda x, y: x + y, bb)
|
||
|
|
# choose preferentially a bottom node.
|
||
|
|
target = seed.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
|
||
|
|
|
||
|
|
|
||
|
|
@py_random_state(3)
|
||
|
|
def random_graph(n, m, p, seed=None, directed=False):
|
||
|
|
"""Returns a bipartite random graph.
|
||
|
|
|
||
|
|
This is a bipartite version of the binomial (Erdős-Rényi) graph.
|
||
|
|
The graph is composed of two partitions. Set A has nodes 0 to
|
||
|
|
(n - 1) and set B has nodes n to (n + m - 1).
|
||
|
|
|
||
|
|
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 : integer, random_state, or None (default)
|
||
|
|
Indicator of random number generation state.
|
||
|
|
See :ref:`Randomness<randomness>`.
|
||
|
|
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.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.random_graph
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
gnp_random_graph, 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 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 - seed.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 - seed.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
|
||
|
|
|
||
|
|
|
||
|
|
@py_random_state(3)
|
||
|
|
def gnmk_random_graph(n, m, k, seed=None, directed=False):
|
||
|
|
"""Returns 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.
|
||
|
|
The graph is composed of two sets of nodes.
|
||
|
|
Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1).
|
||
|
|
|
||
|
|
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 : integer, random_state, or None (default)
|
||
|
|
Indicator of random number generation state.
|
||
|
|
See :ref:`Randomness<randomness>`.
|
||
|
|
directed : bool, optional (default=False)
|
||
|
|
If True return a directed graph
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
from nx.algorithms import bipartite
|
||
|
|
G = 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.
|
||
|
|
|
||
|
|
The nodes are assigned the attribute 'bipartite' with the value 0 or 1
|
||
|
|
to indicate which bipartite set the node belongs to.
|
||
|
|
|
||
|
|
This function is not imported in the main namespace.
|
||
|
|
To use it use nx.bipartite.gnmk_random_graph
|
||
|
|
"""
|
||
|
|
G = nx.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 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 nx.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 = seed.choice(top)
|
||
|
|
v = seed.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, b, 'bipartite')
|
||
|
|
return G
|