/usr/lib/python3/dist-packages/networkx/classes/function.py is in python3-networkx 1.11-1ubuntu2.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 | """Functional interface to graph methods and assorted utilities.
"""
# Copyright (C) 2004-2015 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
import networkx as nx
from networkx.utils import not_implemented_for
import itertools
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
__all__ = ['nodes', 'edges', 'degree', 'degree_histogram', 'neighbors',
'number_of_nodes', 'number_of_edges', 'density',
'nodes_iter', 'edges_iter', 'is_directed','info',
'freeze','is_frozen','subgraph','create_empty_copy',
'set_node_attributes','get_node_attributes',
'set_edge_attributes','get_edge_attributes',
'all_neighbors','non_neighbors', 'non_edges',
'common_neighbors', 'is_weighted','is_negatively_weighted',
'is_empty']
def nodes(G):
"""Return a copy of the graph nodes in a list."""
return G.nodes()
def nodes_iter(G):
"""Return an iterator over the graph nodes."""
return G.nodes_iter()
def edges(G,nbunch=None):
"""Return list of edges incident to nodes in nbunch.
Return all edges if nbunch is unspecified or nbunch=None.
For digraphs, edges=out_edges
"""
return G.edges(nbunch)
def edges_iter(G,nbunch=None):
"""Return iterator over edges incident to nodes in nbunch.
Return all edges if nbunch is unspecified or nbunch=None.
For digraphs, edges=out_edges
"""
return G.edges_iter(nbunch)
def degree(G,nbunch=None,weight=None):
"""Return degree of single node or of nbunch of nodes.
If nbunch is ommitted, then return degrees of *all* nodes.
"""
return G.degree(nbunch,weight)
def neighbors(G,n):
"""Return a list of nodes connected to node n. """
return G.neighbors(n)
def number_of_nodes(G):
"""Return the number of nodes in the graph."""
return G.number_of_nodes()
def number_of_edges(G):
"""Return the number of edges in the graph. """
return G.number_of_edges()
def density(G):
r"""Return the density of a graph.
The density for undirected graphs is
.. math::
d = \frac{2m}{n(n-1)},
and for directed graphs is
.. math::
d = \frac{m}{n(n-1)},
where `n` is the number of nodes and `m` is the number of edges in `G`.
Notes
-----
The density is 0 for a graph without edges and 1 for a complete graph.
The density of multigraphs can be higher than 1.
Self loops are counted in the total number of edges so graphs with self
loops can have density higher than 1.
"""
n=number_of_nodes(G)
m=number_of_edges(G)
if m==0 or n <= 1:
d=0.0
else:
if G.is_directed():
d=m/float(n*(n-1))
else:
d= m*2.0/float(n*(n-1))
return d
def degree_histogram(G):
"""Return a list of the frequency of each degree value.
Parameters
----------
G : Networkx graph
A graph
Returns
-------
hist : list
A list of frequencies of degrees.
The degree values are the index in the list.
Notes
-----
Note: the bins are width one, hence len(list) can be large
(Order(number_of_edges))
"""
degseq=list(G.degree().values())
dmax=max(degseq)+1
freq= [ 0 for d in range(dmax) ]
for d in degseq:
freq[d] += 1
return freq
def is_directed(G):
""" Return True if graph is directed."""
return G.is_directed()
def frozen(*args):
"""Dummy method for raising errors when trying to modify frozen graphs"""
raise nx.NetworkXError("Frozen graph can't be modified")
def freeze(G):
"""Modify graph to prevent further change by adding or removing
nodes or edges.
Node and edge data can still be modified.
Parameters
----------
G : graph
A NetworkX graph
Examples
--------
>>> G=nx.Graph()
>>> G.add_path([0,1,2,3])
>>> G=nx.freeze(G)
>>> try:
... G.add_edge(4,5)
... except nx.NetworkXError as e:
... print(str(e))
Frozen graph can't be modified
Notes
-----
To "unfreeze" a graph you must make a copy by creating a new graph object:
>>> graph = nx.path_graph(4)
>>> frozen_graph = nx.freeze(graph)
>>> unfrozen_graph = nx.Graph(frozen_graph)
>>> nx.is_frozen(unfrozen_graph)
False
See Also
--------
is_frozen
"""
G.add_node=frozen
G.add_nodes_from=frozen
G.remove_node=frozen
G.remove_nodes_from=frozen
G.add_edge=frozen
G.add_edges_from=frozen
G.remove_edge=frozen
G.remove_edges_from=frozen
G.clear=frozen
G.frozen=True
return G
def is_frozen(G):
"""Return True if graph is frozen.
Parameters
----------
G : graph
A NetworkX graph
See Also
--------
freeze
"""
try:
return G.frozen
except AttributeError:
return False
def subgraph(G, nbunch):
"""Return the subgraph induced on nodes in nbunch.
Parameters
----------
G : graph
A NetworkX graph
nbunch : list, iterable
A container of nodes that will be iterated through once (thus
it should be an iterator or be iterable). Each element of the
container should be a valid node type: any hashable type except
None. If nbunch is None, return all edges data in the graph.
Nodes in nbunch that are not in the graph will be (quietly)
ignored.
Notes
-----
subgraph(G) calls G.subgraph()
"""
return G.subgraph(nbunch)
def create_empty_copy(G,with_nodes=True):
"""Return a copy of the graph G with all of the edges removed.
Parameters
----------
G : graph
A NetworkX graph
with_nodes : bool (default=True)
Include nodes.
Notes
-----
Graph, node, and edge data is not propagated to the new graph.
"""
H=G.__class__()
if with_nodes:
H.add_nodes_from(G)
return H
def info(G, n=None):
"""Print short summary of information for the graph G or the node n.
Parameters
----------
G : Networkx graph
A graph
n : node (any hashable)
A node in the graph G
"""
info='' # append this all to a string
if n is None:
info+="Name: %s\n"%G.name
type_name = [type(G).__name__]
info+="Type: %s\n"%",".join(type_name)
info+="Number of nodes: %d\n"%G.number_of_nodes()
info+="Number of edges: %d\n"%G.number_of_edges()
nnodes=G.number_of_nodes()
if len(G) > 0:
if G.is_directed():
info+="Average in degree: %8.4f\n"%\
(sum(G.in_degree().values())/float(nnodes))
info+="Average out degree: %8.4f"%\
(sum(G.out_degree().values())/float(nnodes))
else:
s=sum(G.degree().values())
info+="Average degree: %8.4f"%\
(float(s)/float(nnodes))
else:
if n not in G:
raise nx.NetworkXError("node %s not in graph"%(n,))
info+="Node % s has the following properties:\n"%n
info+="Degree: %d\n"%G.degree(n)
info+="Neighbors: "
info+=' '.join(str(nbr) for nbr in G.neighbors(n))
return info
def set_node_attributes(G, name, values):
"""Set node attributes from dictionary of nodes and values
Parameters
----------
G : NetworkX Graph
name : string
Attribute name
values: dict
Dictionary of attribute values keyed by node. If `values` is not a
dictionary, then it is treated as a single attribute value that is then
applied to every node in `G`.
Examples
--------
>>> G = nx.path_graph(3)
>>> bb = nx.betweenness_centrality(G)
>>> nx.set_node_attributes(G, 'betweenness', bb)
>>> G.node[1]['betweenness']
1.0
"""
try:
values.items
except AttributeError:
# Treat `value` as the attribute value for each node.
values = dict(zip(G.nodes(), [values] * len(G)))
for node, value in values.items():
G.node[node][name] = value
def get_node_attributes(G, name):
"""Get node attributes from graph
Parameters
----------
G : NetworkX Graph
name : string
Attribute name
Returns
-------
Dictionary of attributes keyed by node.
Examples
--------
>>> G=nx.Graph()
>>> G.add_nodes_from([1,2,3],color='red')
>>> color=nx.get_node_attributes(G,'color')
>>> color[1]
'red'
"""
return dict( (n,d[name]) for n,d in G.node.items() if name in d)
def set_edge_attributes(G, name, values):
"""Set edge attributes from dictionary of edge tuples and values.
Parameters
----------
G : NetworkX Graph
name : string
Attribute name
values : dict
Dictionary of attribute values keyed by edge (tuple). For multigraphs,
the keys tuples must be of the form (u, v, key). For non-multigraphs,
the keys must be tuples of the form (u, v). If `values` is not a
dictionary, then it is treated as a single attribute value that is then
applied to every edge in `G`.
Examples
--------
>>> G = nx.path_graph(3)
>>> bb = nx.edge_betweenness_centrality(G, normalized=False)
>>> nx.set_edge_attributes(G, 'betweenness', bb)
>>> G[1][2]['betweenness']
2.0
"""
try:
values.items
except AttributeError:
# Treat `value` as the attribute value for each edge.
if G.is_multigraph():
edges = G.edges(keys=True)
else:
edges = G.edges()
values = dict(zip(edges, [values] * len(edges)))
if G.is_multigraph():
for (u, v, key), value in values.items():
G[u][v][key][name] = value
else:
for (u, v), value in values.items():
G[u][v][name] = value
def get_edge_attributes(G, name):
"""Get edge attributes from graph
Parameters
----------
G : NetworkX Graph
name : string
Attribute name
Returns
-------
Dictionary of attributes keyed by edge. For (di)graphs, the keys are
2-tuples of the form: (u,v). For multi(di)graphs, the keys are 3-tuples of
the form: (u, v, key).
Examples
--------
>>> G=nx.Graph()
>>> G.add_path([1,2,3],color='red')
>>> color=nx.get_edge_attributes(G,'color')
>>> color[(1,2)]
'red'
"""
if G.is_multigraph():
edges = G.edges(keys=True, data=True)
else:
edges = G.edges(data=True)
return dict( (x[:-1], x[-1][name]) for x in edges if name in x[-1] )
def all_neighbors(graph, node):
""" Returns all of the neighbors of a node in the graph.
If the graph is directed returns predecessors as well as successors.
Parameters
----------
graph : NetworkX graph
Graph to find neighbors.
node : node
The node whose neighbors will be returned.
Returns
-------
neighbors : iterator
Iterator of neighbors
"""
if graph.is_directed():
values = itertools.chain.from_iterable([graph.predecessors_iter(node),
graph.successors_iter(node)])
else:
values = graph.neighbors_iter(node)
return values
def non_neighbors(graph, node):
"""Returns the non-neighbors of the node in the graph.
Parameters
----------
graph : NetworkX graph
Graph to find neighbors.
node : node
The node whose neighbors will be returned.
Returns
-------
non_neighbors : iterator
Iterator of nodes in the graph that are not neighbors of the node.
"""
nbors = set(neighbors(graph, node)) | set([node])
return (nnode for nnode in graph if nnode not in nbors)
def non_edges(graph):
"""Returns the non-existent edges in the graph.
Parameters
----------
graph : NetworkX graph.
Graph to find non-existent edges.
Returns
-------
non_edges : iterator
Iterator of edges that are not in the graph.
"""
if graph.is_directed():
for u in graph.nodes_iter():
for v in non_neighbors(graph, u):
yield (u, v)
else:
nodes = set(graph)
while nodes:
u = nodes.pop()
for v in nodes - set(graph[u]):
yield (u, v)
@not_implemented_for('directed')
def common_neighbors(G, u, v):
"""Return the common neighbors of two nodes in a graph.
Parameters
----------
G : graph
A NetworkX undirected graph.
u, v : nodes
Nodes in the graph.
Returns
-------
cnbors : iterator
Iterator of common neighbors of u and v in the graph.
Raises
------
NetworkXError
If u or v is not a node in the graph.
Examples
--------
>>> G = nx.complete_graph(5)
>>> sorted(nx.common_neighbors(G, 0, 1))
[2, 3, 4]
"""
if u not in G:
raise nx.NetworkXError('u is not in the graph.')
if v not in G:
raise nx.NetworkXError('v is not in the graph.')
# Return a generator explicitly instead of yielding so that the above
# checks are executed eagerly.
return (w for w in G[u] if w in G[v] and w not in (u, v))
def is_weighted(G, edge=None, weight='weight'):
"""Returns ``True`` if ``G`` has weighted edges.
Parameters
----------
G : graph
A NetworkX graph.
edge : tuple, optional
A 2-tuple specifying the only edge in ``G`` that will be tested. If
``None``, then every edge in ``G`` is tested.
weight: string, optional
The attribute name used to query for edge weights.
Returns
-------
bool
A boolean signifying if ``G``, or the specified edge, is weighted.
Raises
------
NetworkXError
If the specified edge does not exist.
Examples
--------
>>> G = nx.path_graph(4)
>>> nx.is_weighted(G)
False
>>> nx.is_weighted(G, (2, 3))
False
>>> G = nx.DiGraph()
>>> G.add_edge(1, 2, weight=1)
>>> nx.is_weighted(G)
True
"""
if edge is not None:
data = G.get_edge_data(*edge)
if data is None:
msg = 'Edge {!r} does not exist.'.format(edge)
raise nx.NetworkXError(msg)
return weight in data
if is_empty(G):
# Special handling required since: all([]) == True
return False
return all(weight in data for u, v, data in G.edges(data=True))
def is_negatively_weighted(G, edge=None, weight='weight'):
"""Returns ``True`` if ``G`` has negatively weighted edges.
Parameters
----------
G : graph
A NetworkX graph.
edge : tuple, optional
A 2-tuple specifying the only edge in ``G`` that will be tested. If
``None``, then every edge in ``G`` is tested.
weight: string, optional
The attribute name used to query for edge weights.
Returns
-------
bool
A boolean signifying if ``G``, or the specified edge, is negatively
weighted.
Raises
------
NetworkXError
If the specified edge does not exist.
Examples
--------
>>> G=nx.Graph()
>>> G.add_edges_from([(1, 3), (2, 4), (2, 6)])
>>> G.add_edge(1, 2, weight=4)
>>> nx.is_negatively_weighted(G, (1, 2))
False
>>> G[2][4]['weight'] = -2
>>> nx.is_negatively_weighted(G)
True
>>> G = nx.DiGraph()
>>> G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5), ('1', '0', -2)])
>>> nx.is_negatively_weighted(G)
True
"""
if edge is not None:
data = G.get_edge_data(*edge)
if data is None:
msg = 'Edge {!r} does not exist.'.format(edge)
raise nx.NetworkXError(msg)
return weight in data and data[weight] < 0
return any(weight in data and data[weight] < 0
for u, v, data in G.edges(data=True))
def is_empty(G):
"""Returns ``True`` if ``G`` has no edges.
Parameters
----------
G : graph
A NetworkX graph.
Returns
-------
bool
``True`` if ``G`` has no edges, and ``False`` otherwise.
Notes
-----
An empty graph can have nodes but not edges. The empty graph with zero
nodes is known as the null graph. This is an O(n) operation where n is the
number of nodes in the graph.
"""
return not any(G.adj.values())
|