Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.9/dist-packages/networkx/classes/multidigraph.py: 58%

1"""Base class for MultiDiGraph."""

2from copy import deepcopy

3from functools import cached_property

5import networkx as nx

6from networkx import convert

7from networkx.classes.coreviews import MultiAdjacencyView

8from networkx.classes.digraph import DiGraph

9from networkx.classes.multigraph import MultiGraph

10from networkx.classes.reportviews import (

11 DiMultiDegreeView,

12 InMultiDegreeView,

13 InMultiEdgeView,

14 OutMultiDegreeView,

15 OutMultiEdgeView,

16)

17from networkx.exception import NetworkXError

19__all__ = ["MultiDiGraph"]

22class MultiDiGraph(MultiGraph, DiGraph):

23 """A directed graph class that can store multiedges.

25 Multiedges are multiple edges between two nodes. Each edge

26 can hold optional data or attributes.

28 A MultiDiGraph holds directed edges. Self loops are allowed.

30 Nodes can be arbitrary (hashable) Python objects with optional

31 key/value attributes. By convention `None` is not used as a node.

33 Edges are represented as links between nodes with optional

34 key/value attributes.

36 Parameters

37 ----------

38 incoming_graph_data : input graph (optional, default: None)

39 Data to initialize graph. If None (default) an empty

40 graph is created. The data can be any format that is supported

41 by the to_networkx_graph() function, currently including edge list,

42 dict of dicts, dict of lists, NetworkX graph, 2D NumPy array, SciPy

43 sparse matrix, or PyGraphviz graph.

45 multigraph_input : bool or None (default None)

46 Note: Only used when `incoming_graph_data` is a dict.

47 If True, `incoming_graph_data` is assumed to be a

48 dict-of-dict-of-dict-of-dict structure keyed by

49 node to neighbor to edge keys to edge data for multi-edges.

50 A NetworkXError is raised if this is not the case.

51 If False, :func:`to_networkx_graph` is used to try to determine

52 the dict's graph data structure as either a dict-of-dict-of-dict

53 keyed by node to neighbor to edge data, or a dict-of-iterable

54 keyed by node to neighbors.

55 If None, the treatment for True is tried, but if it fails,

56 the treatment for False is tried.

58 attr : keyword arguments, optional (default= no attributes)

59 Attributes to add to graph as key=value pairs.

61 See Also

62 --------

63 Graph

64 DiGraph

65 MultiGraph

67 Examples

68 --------

69 Create an empty graph structure (a "null graph") with no nodes and

70 no edges.

72 >>> G = nx.MultiDiGraph()

74 G can be grown in several ways.

76 **Nodes:**

78 Add one node at a time:

80 >>> G.add_node(1)

82 Add the nodes from any container (a list, dict, set or

83 even the lines from a file or the nodes from another graph).

85 >>> G.add_nodes_from([2, 3])

86 >>> G.add_nodes_from(range(100, 110))

87 >>> H = nx.path_graph(10)

88 >>> G.add_nodes_from(H)

90 In addition to strings and integers any hashable Python object

91 (except None) can represent a node, e.g. a customized node object,

92 or even another Graph.

94 >>> G.add_node(H)

96 **Edges:**

98 G can also be grown by adding edges.

100 Add one edge,

101

102 >>> key = G.add_edge(1, 2)

103

104 a list of edges,

105

106 >>> keys = G.add_edges_from([(1, 2), (1, 3)])

107

108 or a collection of edges,

109

110 >>> keys = G.add_edges_from(H.edges)

111

112 If some edges connect nodes not yet in the graph, the nodes

113 are added automatically. If an edge already exists, an additional

114 edge is created and stored using a key to identify the edge.

115 By default the key is the lowest unused integer.

116

117 >>> keys = G.add_edges_from([(4, 5, dict(route=282)), (4, 5, dict(route=37))])

118 >>> G[4]

119 AdjacencyView({5: {0: {}, 1: {'route': 282}, 2: {'route': 37}}})

120

121 **Attributes:**

122

123 Each graph, node, and edge can hold key/value attribute pairs

124 in an associated attribute dictionary (the keys must be hashable).

125 By default these are empty, but can be added or changed using

126 add_edge, add_node or direct manipulation of the attribute

127 dictionaries named graph, node and edge respectively.

128

129 >>> G = nx.MultiDiGraph(day="Friday")

130 >>> G.graph

131 {'day': 'Friday'}

132

133 Add node attributes using add_node(), add_nodes_from() or G.nodes

134

135 >>> G.add_node(1, time="5pm")

136 >>> G.add_nodes_from([3], time="2pm")

137 >>> G.nodes[1]

138 {'time': '5pm'}

139 >>> G.nodes[1]["room"] = 714

140 >>> del G.nodes[1]["room"] # remove attribute

141 >>> list(G.nodes(data=True))

142 [(1, {'time': '5pm'}), (3, {'time': '2pm'})]

143

144 Add edge attributes using add_edge(), add_edges_from(), subscript

145 notation, or G.edges.

146

147 >>> key = G.add_edge(1, 2, weight=4.7)

148 >>> keys = G.add_edges_from([(3, 4), (4, 5)], color="red")

149 >>> keys = G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})])

150 >>> G[1][2][0]["weight"] = 4.7

151 >>> G.edges[1, 2, 0]["weight"] = 4

152

153 Warning: we protect the graph data structure by making `G.edges[1,

154 2, 0]` a read-only dict-like structure. However, you can assign to

155 attributes in e.g. `G.edges[1, 2, 0]`. Thus, use 2 sets of brackets

156 to add/change data attributes: `G.edges[1, 2, 0]['weight'] = 4`

157 (for multigraphs the edge key is required: `MG.edges[u, v,

158 key][name] = value`).

159

160 **Shortcuts:**

161

162 Many common graph features allow python syntax to speed reporting.

163

164 >>> 1 in G # check if node in graph

165 True

166 >>> [n for n in G if n < 3] # iterate through nodes

167 [1, 2]

168 >>> len(G) # number of nodes in graph

169 5

170 >>> G[1] # adjacency dict-like view mapping neighbor -> edge key -> edge attributes

171 AdjacencyView({2: {0: {'weight': 4}, 1: {'color': 'blue'}}})

172

173 Often the best way to traverse all edges of a graph is via the neighbors.

174 The neighbors are available as an adjacency-view `G.adj` object or via

175 the method `G.adjacency()`.

176

177 >>> for n, nbrsdict in G.adjacency():

178 ... for nbr, keydict in nbrsdict.items():

179 ... for key, eattr in keydict.items():

180 ... if "weight" in eattr:

181 ... # Do something useful with the edges

182 ... pass

183

184 But the edges() method is often more convenient:

185

186 >>> for u, v, keys, weight in G.edges(data="weight", keys=True):

187 ... if weight is not None:

188 ... # Do something useful with the edges

189 ... pass

190

191 **Reporting:**

192

193 Simple graph information is obtained using methods and object-attributes.

194 Reporting usually provides views instead of containers to reduce memory

195 usage. The views update as the graph is updated similarly to dict-views.

196 The objects `nodes`, `edges` and `adj` provide access to data attributes

197 via lookup (e.g. `nodes[n]`, `edges[u, v, k]`, `adj[u][v]`) and iteration

198 (e.g. `nodes.items()`, `nodes.data('color')`,

199 `nodes.data('color', default='blue')` and similarly for `edges`)

200 Views exist for `nodes`, `edges`, `neighbors()`/`adj` and `degree`.

201

202 For details on these and other miscellaneous methods, see below.

203

204 **Subclasses (Advanced):**

205

206 The MultiDiGraph class uses a dict-of-dict-of-dict-of-dict structure.

207 The outer dict (node_dict) holds adjacency information keyed by node.

208 The next dict (adjlist_dict) represents the adjacency information

209 and holds edge_key dicts keyed by neighbor. The edge_key dict holds

210 each edge_attr dict keyed by edge key. The inner dict

211 (edge_attr_dict) represents the edge data and holds edge attribute

212 values keyed by attribute names.

213

214 Each of these four dicts in the dict-of-dict-of-dict-of-dict

215 structure can be replaced by a user defined dict-like object.

216 In general, the dict-like features should be maintained but

217 extra features can be added. To replace one of the dicts create

218 a new graph class by changing the class(!) variable holding the

219 factory for that dict-like structure. The variable names are

220 node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory,

221 adjlist_outer_dict_factory, edge_key_dict_factory, edge_attr_dict_factory

222 and graph_attr_dict_factory.

223

224 node_dict_factory : function, (default: dict)

225 Factory function to be used to create the dict containing node

226 attributes, keyed by node id.

227 It should require no arguments and return a dict-like object

228

229 node_attr_dict_factory: function, (default: dict)

230 Factory function to be used to create the node attribute

231 dict which holds attribute values keyed by attribute name.

232 It should require no arguments and return a dict-like object

233

234 adjlist_outer_dict_factory : function, (default: dict)

235 Factory function to be used to create the outer-most dict

236 in the data structure that holds adjacency info keyed by node.

237 It should require no arguments and return a dict-like object.

238

239 adjlist_inner_dict_factory : function, (default: dict)

240 Factory function to be used to create the adjacency list

241 dict which holds multiedge key dicts keyed by neighbor.

242 It should require no arguments and return a dict-like object.

243

244 edge_key_dict_factory : function, (default: dict)

245 Factory function to be used to create the edge key dict

246 which holds edge data keyed by edge key.

247 It should require no arguments and return a dict-like object.

248

249 edge_attr_dict_factory : function, (default: dict)

250 Factory function to be used to create the edge attribute

251 dict which holds attribute values keyed by attribute name.

252 It should require no arguments and return a dict-like object.

253

254 graph_attr_dict_factory : function, (default: dict)

255 Factory function to be used to create the graph attribute

256 dict which holds attribute values keyed by attribute name.

257 It should require no arguments and return a dict-like object.

258

259 Typically, if your extension doesn't impact the data structure all

260 methods will inherited without issue except: `to_directed/to_undirected`.

261 By default these methods create a DiGraph/Graph class and you probably

262 want them to create your extension of a DiGraph/Graph. To facilitate

263 this we define two class variables that you can set in your subclass.

264

265 to_directed_class : callable, (default: DiGraph or MultiDiGraph)

266 Class to create a new graph structure in the `to_directed` method.

267 If `None`, a NetworkX class (DiGraph or MultiDiGraph) is used.

268

269 to_undirected_class : callable, (default: Graph or MultiGraph)

270 Class to create a new graph structure in the `to_undirected` method.

271 If `None`, a NetworkX class (Graph or MultiGraph) is used.

272

273 **Subclassing Example**

274

275 Create a low memory graph class that effectively disallows edge

276 attributes by using a single attribute dict for all edges.

277 This reduces the memory used, but you lose edge attributes.

278

279 >>> class ThinGraph(nx.Graph):

280 ... all_edge_dict = {"weight": 1}

281 ...

282 ... def single_edge_dict(self):

283 ... return self.all_edge_dict

284 ...

285 ... edge_attr_dict_factory = single_edge_dict

286 >>> G = ThinGraph()

287 >>> G.add_edge(2, 1)

288 >>> G[2][1]

289 {'weight': 1}

290 >>> G.add_edge(2, 2)

291 >>> G[2][1] is G[2][2]

292 True

293 """

294

295 # node_dict_factory = dict # already assigned in Graph

296 # adjlist_outer_dict_factory = dict

297 # adjlist_inner_dict_factory = dict

298 edge_key_dict_factory = dict

299 # edge_attr_dict_factory = dict

300

301 def __init__(self, incoming_graph_data=None, multigraph_input=None, **attr):

302 """Initialize a graph with edges, name, or graph attributes.

303

304 Parameters

305 ----------

306 incoming_graph_data : input graph

307 Data to initialize graph. If incoming_graph_data=None (default)

308 an empty graph is created. The data can be an edge list, or any

309 NetworkX graph object. If the corresponding optional Python

310 packages are installed the data can also be a 2D NumPy array, a

311 SciPy sparse array, or a PyGraphviz graph.

312

313 multigraph_input : bool or None (default None)

314 Note: Only used when `incoming_graph_data` is a dict.

315 If True, `incoming_graph_data` is assumed to be a

316 dict-of-dict-of-dict-of-dict structure keyed by

317 node to neighbor to edge keys to edge data for multi-edges.

318 A NetworkXError is raised if this is not the case.

319 If False, :func:`to_networkx_graph` is used to try to determine

320 the dict's graph data structure as either a dict-of-dict-of-dict

321 keyed by node to neighbor to edge data, or a dict-of-iterable

322 keyed by node to neighbors.

323 If None, the treatment for True is tried, but if it fails,

324 the treatment for False is tried.

325

326 attr : keyword arguments, optional (default= no attributes)

327 Attributes to add to graph as key=value pairs.

328

329 See Also

330 --------

331 convert

332

333 Examples

334 --------

335 >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc

336 >>> G = nx.Graph(name="my graph")

337 >>> e = [(1, 2), (2, 3), (3, 4)] # list of edges

338 >>> G = nx.Graph(e)

339

340 Arbitrary graph attribute pairs (key=value) may be assigned

341

342 >>> G = nx.Graph(e, day="Friday")

343 >>> G.graph

344 {'day': 'Friday'}

345

346 """

347 # multigraph_input can be None/True/False. So check "is not False"

348 if isinstance(incoming_graph_data, dict) and multigraph_input is not False:

349 DiGraph.__init__(self)

350 try:

351 convert.from_dict_of_dicts(

352 incoming_graph_data, create_using=self, multigraph_input=True

353 )

354 self.graph.update(attr)

355 except Exception as err:

356 if multigraph_input is True:

357 raise nx.NetworkXError(

358 f"converting multigraph_input raised:\n{type(err)}: {err}"

359 )

360 DiGraph.__init__(self, incoming_graph_data, **attr)

361 else:

362 DiGraph.__init__(self, incoming_graph_data, **attr)

363

364 @cached_property

365 def adj(self):

366 """Graph adjacency object holding the neighbors of each node.

367

368 This object is a read-only dict-like structure with node keys

369 and neighbor-dict values. The neighbor-dict is keyed by neighbor

370 to the edgekey-dict. So `G.adj[3][2][0]['color'] = 'blue'` sets

371 the color of the edge `(3, 2, 0)` to `"blue"`.

372

373 Iterating over G.adj behaves like a dict. Useful idioms include

374 `for nbr, datadict in G.adj[n].items():`.

375

376 The neighbor information is also provided by subscripting the graph.

377 So `for nbr, foovalue in G[node].data('foo', default=1):` works.

378

379 For directed graphs, `G.adj` holds outgoing (successor) info.

380 """

381 return MultiAdjacencyView(self._succ)

382

383 @cached_property

384 def succ(self):

385 """Graph adjacency object holding the successors of each node.

386

387 This object is a read-only dict-like structure with node keys

388 and neighbor-dict values. The neighbor-dict is keyed by neighbor

389 to the edgekey-dict. So `G.adj[3][2][0]['color'] = 'blue'` sets

390 the color of the edge `(3, 2, 0)` to `"blue"`.

391

392 Iterating over G.adj behaves like a dict. Useful idioms include

393 `for nbr, datadict in G.adj[n].items():`.

394

395 The neighbor information is also provided by subscripting the graph.

396 So `for nbr, foovalue in G[node].data('foo', default=1):` works.

397

398 For directed graphs, `G.succ` is identical to `G.adj`.

399 """

400 return MultiAdjacencyView(self._succ)

401

402 @cached_property

403 def pred(self):

404 """Graph adjacency object holding the predecessors of each node.

405

406 This object is a read-only dict-like structure with node keys

407 and neighbor-dict values. The neighbor-dict is keyed by neighbor

408 to the edgekey-dict. So `G.adj[3][2][0]['color'] = 'blue'` sets

409 the color of the edge `(3, 2, 0)` to `"blue"`.

410

411 Iterating over G.adj behaves like a dict. Useful idioms include

412 `for nbr, datadict in G.adj[n].items():`.

413 """

414 return MultiAdjacencyView(self._pred)

415

416 def add_edge(self, u_for_edge, v_for_edge, key=None, **attr):

417 """Add an edge between u and v.

418

419 The nodes u and v will be automatically added if they are

420 not already in the graph.

421

422 Edge attributes can be specified with keywords or by directly

423 accessing the edge's attribute dictionary. See examples below.

424

425 Parameters

426 ----------

427 u_for_edge, v_for_edge : nodes

428 Nodes can be, for example, strings or numbers.

429 Nodes must be hashable (and not None) Python objects.

430 key : hashable identifier, optional (default=lowest unused integer)

431 Used to distinguish multiedges between a pair of nodes.

432 attr : keyword arguments, optional

433 Edge data (or labels or objects) can be assigned using

434 keyword arguments.

435

436 Returns

437 -------

438 The edge key assigned to the edge.

439

440 See Also

441 --------

442 add_edges_from : add a collection of edges

443

444 Notes

445 -----

446 To replace/update edge data, use the optional key argument

447 to identify a unique edge. Otherwise a new edge will be created.

448

449 NetworkX algorithms designed for weighted graphs cannot use

450 multigraphs directly because it is not clear how to handle

451 multiedge weights. Convert to Graph using edge attribute

452 'weight' to enable weighted graph algorithms.

453

454 Default keys are generated using the method `new_edge_key()`.

455 This method can be overridden by subclassing the base class and

456 providing a custom `new_edge_key()` method.

457

458 Examples

459 --------

460 The following all add the edge e=(1, 2) to graph G:

461

462 >>> G = nx.MultiDiGraph()

463 >>> e = (1, 2)

464 >>> key = G.add_edge(1, 2) # explicit two-node form

465 >>> G.add_edge(*e) # single edge as tuple of two nodes

466 1

467 >>> G.add_edges_from([(1, 2)]) # add edges from iterable container

468 [2]

469

470 Associate data to edges using keywords:

471

472 >>> key = G.add_edge(1, 2, weight=3)

473 >>> key = G.add_edge(1, 2, key=0, weight=4) # update data for key=0

474 >>> key = G.add_edge(1, 3, weight=7, capacity=15, length=342.7)

475

476 For non-string attribute keys, use subscript notation.

477

478 >>> ekey = G.add_edge(1, 2)

479 >>> G[1][2][0].update({0: 5})

480 >>> G.edges[1, 2, 0].update({0: 5})

481 """

482 u, v = u_for_edge, v_for_edge

483 # add nodes

484 if u not in self._succ:

485 if u is None:

486 raise ValueError("None cannot be a node")

487 self._succ[u] = self.adjlist_inner_dict_factory()

488 self._pred[u] = self.adjlist_inner_dict_factory()

489 self._node[u] = self.node_attr_dict_factory()

490 if v not in self._succ:

491 if v is None:

492 raise ValueError("None cannot be a node")

493 self._succ[v] = self.adjlist_inner_dict_factory()

494 self._pred[v] = self.adjlist_inner_dict_factory()

495 self._node[v] = self.node_attr_dict_factory()

496 if key is None:

497 key = self.new_edge_key(u, v)

498 if v in self._succ[u]:

499 keydict = self._adj[u][v]

500 datadict = keydict.get(key, self.edge_attr_dict_factory())

501 datadict.update(attr)

502 keydict[key] = datadict

503 else:

504 # selfloops work this way without special treatment

505 datadict = self.edge_attr_dict_factory()

506 datadict.update(attr)

507 keydict = self.edge_key_dict_factory()

508 keydict[key] = datadict

509 self._succ[u][v] = keydict

510 self._pred[v][u] = keydict

511 return key

512

513 def remove_edge(self, u, v, key=None):

514 """Remove an edge between u and v.

515

516 Parameters

517 ----------

518 u, v : nodes

519 Remove an edge between nodes u and v.

520 key : hashable identifier, optional (default=None)

521 Used to distinguish multiple edges between a pair of nodes.

522 If None, remove a single edge between u and v. If there are

523 multiple edges, removes the last edge added in terms of

524 insertion order.

525

526 Raises

527 ------

528 NetworkXError

529 If there is not an edge between u and v, or

530 if there is no edge with the specified key.

531

532 See Also

533 --------

534 remove_edges_from : remove a collection of edges

535

536 Examples

537 --------

538 >>> G = nx.MultiDiGraph()

539 >>> nx.add_path(G, [0, 1, 2, 3])

540 >>> G.remove_edge(0, 1)

541 >>> e = (1, 2)

542 >>> G.remove_edge(*e) # unpacks e from an edge tuple

543

544 For multiple edges

545

546 >>> G = nx.MultiDiGraph()

547 >>> G.add_edges_from([(1, 2), (1, 2), (1, 2)]) # key_list returned

548 [0, 1, 2]

549

550 When ``key=None`` (the default), edges are removed in the opposite

551 order that they were added:

552

553 >>> G.remove_edge(1, 2)

554 >>> G.edges(keys=True)

555 OutMultiEdgeView([(1, 2, 0), (1, 2, 1)])

556

557 For edges with keys

558

559 >>> G = nx.MultiDiGraph()

560 >>> G.add_edge(1, 2, key="first")

561 'first'

562 >>> G.add_edge(1, 2, key="second")

563 'second'

564 >>> G.remove_edge(1, 2, key="first")

565 >>> G.edges(keys=True)

566 OutMultiEdgeView([(1, 2, 'second')])

567

568 """

569 try:

570 d = self._adj[u][v]

571 except KeyError as err:

572 raise NetworkXError(f"The edge {u}-{v} is not in the graph.") from err

573 # remove the edge with specified data

574 if key is None:

575 d.popitem()

576 else:

577 try:

578 del d[key]

579 except KeyError as err:

580 msg = f"The edge {u}-{v} with key {key} is not in the graph."

581 raise NetworkXError(msg) from err

582 if len(d) == 0:

583 # remove the key entries if last edge

584 del self._succ[u][v]

585 del self._pred[v][u]

586

587 @cached_property

588 def edges(self):

589 """An OutMultiEdgeView of the Graph as G.edges or G.edges().

590

591 edges(self, nbunch=None, data=False, keys=False, default=None)

592

593 The OutMultiEdgeView provides set-like operations on the edge-tuples

594 as well as edge attribute lookup. When called, it also provides

595 an EdgeDataView object which allows control of access to edge

596 attributes (but does not provide set-like operations).

597 Hence, ``G.edges[u, v, k]['color']`` provides the value of the color

598 attribute for the edge from ``u`` to ``v`` with key ``k`` while

599 ``for (u, v, k, c) in G.edges(data='color', default='red', keys=True):``

600 iterates through all the edges yielding the color attribute with

601 default `'red'` if no color attribute exists.

602

603 Edges are returned as tuples with optional data and keys

604 in the order (node, neighbor, key, data). If ``keys=True`` is not

605 provided, the tuples will just be (node, neighbor, data), but

606 multiple tuples with the same node and neighbor will be

607 generated when multiple edges between two nodes exist.

608

609 Parameters

610 ----------

611 nbunch : single node, container, or all nodes (default= all nodes)

612 The view will only report edges from these nodes.

613 data : string or bool, optional (default=False)

614 The edge attribute returned in 3-tuple (u, v, ddict[data]).

615 If True, return edge attribute dict in 3-tuple (u, v, ddict).

616 If False, return 2-tuple (u, v).

617 keys : bool, optional (default=False)

618 If True, return edge keys with each edge, creating (u, v, k,

619 d) tuples when data is also requested (the default) and (u,

620 v, k) tuples when data is not requested.

621 default : value, optional (default=None)

622 Value used for edges that don't have the requested attribute.

623 Only relevant if data is not True or False.

624

625 Returns

626 -------

627 edges : OutMultiEdgeView

628 A view of edge attributes, usually it iterates over (u, v)

629 (u, v, k) or (u, v, k, d) tuples of edges, but can also be

630 used for attribute lookup as ``edges[u, v, k]['foo']``.

631

632 Notes

633 -----

634 Nodes in nbunch that are not in the graph will be (quietly) ignored.

635 For directed graphs this returns the out-edges.

636

637 Examples

638 --------

639 >>> G = nx.MultiDiGraph()

640 >>> nx.add_path(G, [0, 1, 2])

641 >>> key = G.add_edge(2, 3, weight=5)

642 >>> key2 = G.add_edge(1, 2) # second edge between these nodes

643 >>> [e for e in G.edges()]

644 [(0, 1), (1, 2), (1, 2), (2, 3)]

645 >>> list(G.edges(data=True)) # default data is {} (empty dict)

646 [(0, 1, {}), (1, 2, {}), (1, 2, {}), (2, 3, {'weight': 5})]

647 >>> list(G.edges(data="weight", default=1))

648 [(0, 1, 1), (1, 2, 1), (1, 2, 1), (2, 3, 5)]

649 >>> list(G.edges(keys=True)) # default keys are integers

650 [(0, 1, 0), (1, 2, 0), (1, 2, 1), (2, 3, 0)]

651 >>> list(G.edges(data=True, keys=True))

652 [(0, 1, 0, {}), (1, 2, 0, {}), (1, 2, 1, {}), (2, 3, 0, {'weight': 5})]

653 >>> list(G.edges(data="weight", default=1, keys=True))

654 [(0, 1, 0, 1), (1, 2, 0, 1), (1, 2, 1, 1), (2, 3, 0, 5)]

655 >>> list(G.edges([0, 2]))

656 [(0, 1), (2, 3)]

657 >>> list(G.edges(0))

658 [(0, 1)]

659 >>> list(G.edges(1))

660 [(1, 2), (1, 2)]

661

662 See Also

663 --------

664 in_edges, out_edges

665 """

666 return OutMultiEdgeView(self)

667

668 # alias out_edges to edges

669 @cached_property

670 def out_edges(self):

671 return OutMultiEdgeView(self)

672

673 out_edges.__doc__ = edges.__doc__

674

675 @cached_property

676 def in_edges(self):

677 """A view of the in edges of the graph as G.in_edges or G.in_edges().

678

679 in_edges(self, nbunch=None, data=False, keys=False, default=None)

680

681 Parameters

682 ----------

683 nbunch : single node, container, or all nodes (default= all nodes)

684 The view will only report edges incident to these nodes.

685 data : string or bool, optional (default=False)

686 The edge attribute returned in 3-tuple (u, v, ddict[data]).

687 If True, return edge attribute dict in 3-tuple (u, v, ddict).

688 If False, return 2-tuple (u, v).

689 keys : bool, optional (default=False)

690 If True, return edge keys with each edge, creating 3-tuples

691 (u, v, k) or with data, 4-tuples (u, v, k, d).

692 default : value, optional (default=None)

693 Value used for edges that don't have the requested attribute.

694 Only relevant if data is not True or False.

695

696 Returns

697 -------

698 in_edges : InMultiEdgeView or InMultiEdgeDataView

699 A view of edge attributes, usually it iterates over (u, v)

700 or (u, v, k) or (u, v, k, d) tuples of edges, but can also be

701 used for attribute lookup as `edges[u, v, k]['foo']`.

702

703 See Also

704 --------

705 edges

706 """

707 return InMultiEdgeView(self)

708

709 @cached_property

710 def degree(self):

711 """A DegreeView for the Graph as G.degree or G.degree().

712

713 The node degree is the number of edges adjacent to the node.

714 The weighted node degree is the sum of the edge weights for

715 edges incident to that node.

716

717 This object provides an iterator for (node, degree) as well as

718 lookup for the degree for a single node.

719

720 Parameters

721 ----------

722 nbunch : single node, container, or all nodes (default= all nodes)

723 The view will only report edges incident to these nodes.

724

725 weight : string or None, optional (default=None)

726 The name of an edge attribute that holds the numerical value used

727 as a weight. If None, then each edge has weight 1.

728 The degree is the sum of the edge weights adjacent to the node.

729

730 Returns

731 -------

732 DiMultiDegreeView or int

733 If multiple nodes are requested (the default), returns a `DiMultiDegreeView`

734 mapping nodes to their degree.

735 If a single node is requested, returns the degree of the node as an integer.

736

737 See Also

738 --------

739 out_degree, in_degree

740

741 Examples

742 --------

743 >>> G = nx.MultiDiGraph()

744 >>> nx.add_path(G, [0, 1, 2, 3])

745 >>> G.degree(0) # node 0 with degree 1

746 1

747 >>> list(G.degree([0, 1, 2]))

748 [(0, 1), (1, 2), (2, 2)]

749 >>> G.add_edge(0, 1) # parallel edge

750 1

751 >>> list(G.degree([0, 1, 2])) # parallel edges are counted

752 [(0, 2), (1, 3), (2, 2)]

753

754 """

755 return DiMultiDegreeView(self)

756

757 @cached_property

758 def in_degree(self):

759 """A DegreeView for (node, in_degree) or in_degree for single node.

760

761 The node in-degree is the number of edges pointing into the node.

762 The weighted node degree is the sum of the edge weights for

763 edges incident to that node.

764

765 This object provides an iterator for (node, degree) as well as

766 lookup for the degree for a single node.

767

768 Parameters

769 ----------

770 nbunch : single node, container, or all nodes (default= all nodes)

771 The view will only report edges incident to these nodes.

772

773 weight : string or None, optional (default=None)

774 The edge attribute that holds the numerical value used

775 as a weight. If None, then each edge has weight 1.

776 The degree is the sum of the edge weights adjacent to the node.

777

778 Returns

779 -------

780 If a single node is requested

781 deg : int

782 Degree of the node

783

784 OR if multiple nodes are requested

785 nd_iter : iterator

786 The iterator returns two-tuples of (node, in-degree).

787

788 See Also

789 --------

790 degree, out_degree

791

792 Examples

793 --------

794 >>> G = nx.MultiDiGraph()

795 >>> nx.add_path(G, [0, 1, 2, 3])

796 >>> G.in_degree(0) # node 0 with degree 0

797 0

798 >>> list(G.in_degree([0, 1, 2]))

799 [(0, 0), (1, 1), (2, 1)]

800 >>> G.add_edge(0, 1) # parallel edge

801 1

802 >>> list(G.in_degree([0, 1, 2])) # parallel edges counted

803 [(0, 0), (1, 2), (2, 1)]

804

805 """

806 return InMultiDegreeView(self)

807

808 @cached_property

809 def out_degree(self):

810 """Returns an iterator for (node, out-degree) or out-degree for single node.

811

812 out_degree(self, nbunch=None, weight=None)

813

814 The node out-degree is the number of edges pointing out of the node.

815 This function returns the out-degree for a single node or an iterator

816 for a bunch of nodes or if nothing is passed as argument.

817

818 Parameters

819 ----------

820 nbunch : single node, container, or all nodes (default= all nodes)

821 The view will only report edges incident to these nodes.

822

823 weight : string or None, optional (default=None)

824 The edge attribute that holds the numerical value used

825 as a weight. If None, then each edge has weight 1.

826 The degree is the sum of the edge weights.

827

828 Returns

829 -------

830 If a single node is requested

831 deg : int

832 Degree of the node

833

834 OR if multiple nodes are requested

835 nd_iter : iterator

836 The iterator returns two-tuples of (node, out-degree).

837

838 See Also

839 --------

840 degree, in_degree

841

842 Examples

843 --------

844 >>> G = nx.MultiDiGraph()

845 >>> nx.add_path(G, [0, 1, 2, 3])

846 >>> G.out_degree(0) # node 0 with degree 1

847 1

848 >>> list(G.out_degree([0, 1, 2]))

849 [(0, 1), (1, 1), (2, 1)]

850 >>> G.add_edge(0, 1) # parallel edge

851 1

852 >>> list(G.out_degree([0, 1, 2])) # counts parallel edges

853 [(0, 2), (1, 1), (2, 1)]

854

855 """

856 return OutMultiDegreeView(self)

857

858 def is_multigraph(self):

859 """Returns True if graph is a multigraph, False otherwise."""

860 return True

861

862 def is_directed(self):

863 """Returns True if graph is directed, False otherwise."""

864 return True

865

866 def to_undirected(self, reciprocal=False, as_view=False):

867 """Returns an undirected representation of the digraph.

868

869 Parameters

870 ----------

871 reciprocal : bool (optional)

872 If True only keep edges that appear in both directions

873 in the original digraph.

874 as_view : bool (optional, default=False)

875 If True return an undirected view of the original directed graph.

876

877 Returns

878 -------

879 G : MultiGraph

880 An undirected graph with the same name and nodes and

881 with edge (u, v, data) if either (u, v, data) or (v, u, data)

882 is in the digraph. If both edges exist in digraph and

883 their edge data is different, only one edge is created

884 with an arbitrary choice of which edge data to use.

885 You must check and correct for this manually if desired.

886

887 See Also

888 --------

889 MultiGraph, copy, add_edge, add_edges_from

890

891 Notes

892 -----

893 This returns a "deepcopy" of the edge, node, and

894 graph attributes which attempts to completely copy

895 all of the data and references.

896

897 This is in contrast to the similar D=MultiDiGraph(G) which

898 returns a shallow copy of the data.

899

900 See the Python copy module for more information on shallow

901 and deep copies, https://docs.python.org/3/library/copy.html.

902

903 Warning: If you have subclassed MultiDiGraph to use dict-like

904 objects in the data structure, those changes do not transfer

905 to the MultiGraph created by this method.

906

907 Examples

908 --------

909 >>> G = nx.path_graph(2) # or MultiGraph, etc

910 >>> H = G.to_directed()

911 >>> list(H.edges)

912 [(0, 1), (1, 0)]

913 >>> G2 = H.to_undirected()

914 >>> list(G2.edges)

915 [(0, 1)]

916 """

917 graph_class = self.to_undirected_class()

918 if as_view is True:

919 return nx.graphviews.generic_graph_view(self, graph_class)

920 # deepcopy when not a view

921 G = graph_class()

922 G.graph.update(deepcopy(self.graph))

923 G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())

924 if reciprocal is True:

925 G.add_edges_from(

926 (u, v, key, deepcopy(data))

927 for u, nbrs in self._adj.items()

928 for v, keydict in nbrs.items()

929 for key, data in keydict.items()

930 if v in self._pred[u] and key in self._pred[u][v]

931 )

932 else:

933 G.add_edges_from(

934 (u, v, key, deepcopy(data))

935 for u, nbrs in self._adj.items()

936 for v, keydict in nbrs.items()

937 for key, data in keydict.items()

938 )

939 return G

940

941 def reverse(self, copy=True):

942 """Returns the reverse of the graph.

943

944 The reverse is a graph with the same nodes and edges

945 but with the directions of the edges reversed.

946

947 Parameters

948 ----------

949 copy : bool optional (default=True)

950 If True, return a new DiGraph holding the reversed edges.

951 If False, the reverse graph is created using a view of

952 the original graph.

953 """

954 if copy:

955 H = self.__class__()

956 H.graph.update(deepcopy(self.graph))

957 H.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items())

958 H.add_edges_from(

959 (v, u, k, deepcopy(d))

960 for u, v, k, d in self.edges(keys=True, data=True)

961 )

962 return H

963 return nx.reverse_view(self)