/usr/lib/python2.7/dist-packages/networkx/generators/bipartite.py is in python-networkx 1.9+dfsg1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 | # -*- 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',
]
def bipartite_configuration_model(aseq, bseq, create_using=None, seed=None):
"""Return 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, 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
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
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.
"""
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
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
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.
"""
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
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
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.
"""
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
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
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
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
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
|