Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

Source code for networkx.classes.multigraph

"""Base class for MultiGraph."""
from copy import deepcopy

import networkx as nx
from networkx.classes.graph import Graph
from networkx.classes.coreviews import MultiAdjacencyView
from networkx.classes.reportviews import MultiEdgeView, MultiDegreeView
from networkx import NetworkXError


[docs]class MultiGraph(Graph): """ An undirected graph class that can store multiedges. Multiedges are multiple edges between two nodes. Each edge can hold optional data or attributes. A MultiGraph holds undirected edges. Self loops are allowed. Nodes can be arbitrary (hashable) Python objects with optional key/value attributes. By convention `None` is not used as a node. Edges are represented as links between nodes with optional key/value attributes. Parameters ---------- incoming_graph_data : input graph (optional, default: None) Data to initialize graph. If None (default) an empty graph is created. The data can be any format that is supported by the to_networkx_graph() function, currently including edge list, dict of dicts, dict of lists, NetworkX graph, NumPy matrix or 2d ndarray, SciPy sparse matrix, or PyGraphviz graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to graph as key=value pairs. See Also -------- Graph DiGraph MultiDiGraph OrderedMultiGraph Examples -------- Create an empty graph structure (a "null graph") with no nodes and no edges. >>> G = nx.MultiGraph() G can be grown in several ways. **Nodes:** Add one node at a time: >>> G.add_node(1) Add the nodes from any container (a list, dict, set or even the lines from a file or the nodes from another graph). >>> G.add_nodes_from([2, 3]) >>> G.add_nodes_from(range(100, 110)) >>> H = nx.path_graph(10) >>> G.add_nodes_from(H) In addition to strings and integers any hashable Python object (except None) can represent a node, e.g. a customized node object, or even another Graph. >>> G.add_node(H) **Edges:** G can also be grown by adding edges. Add one edge, >>> key = G.add_edge(1, 2) a list of edges, >>> keys = G.add_edges_from([(1, 2), (1, 3)]) or a collection of edges, >>> keys = G.add_edges_from(H.edges) If some edges connect nodes not yet in the graph, the nodes are added automatically. If an edge already exists, an additional edge is created and stored using a key to identify the edge. By default the key is the lowest unused integer. >>> keys = G.add_edges_from([(4, 5, {"route": 28}), (4, 5, {"route": 37})]) >>> G[4] AdjacencyView({3: {0: {}}, 5: {0: {}, 1: {'route': 28}, 2: {'route': 37}}}) **Attributes:** Each graph, node, and edge can hold key/value attribute pairs in an associated attribute dictionary (the keys must be hashable). By default these are empty, but can be added or changed using add_edge, add_node or direct manipulation of the attribute dictionaries named graph, node and edge respectively. >>> G = nx.MultiGraph(day="Friday") >>> G.graph {'day': 'Friday'} Add node attributes using add_node(), add_nodes_from() or G.nodes >>> G.add_node(1, time="5pm") >>> G.add_nodes_from([3], time="2pm") >>> G.nodes[1] {'time': '5pm'} >>> G.nodes[1]["room"] = 714 >>> del G.nodes[1]["room"] # remove attribute >>> list(G.nodes(data=True)) [(1, {'time': '5pm'}), (3, {'time': '2pm'})] Add edge attributes using add_edge(), add_edges_from(), subscript notation, or G.edges. >>> key = G.add_edge(1, 2, weight=4.7) >>> keys = G.add_edges_from([(3, 4), (4, 5)], color="red") >>> keys = G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})]) >>> G[1][2][0]["weight"] = 4.7 >>> G.edges[1, 2, 0]["weight"] = 4 Warning: we protect the graph data structure by making `G.edges[1, 2]` a read-only dict-like structure. However, you can assign to attributes in e.g. `G.edges[1, 2]`. Thus, use 2 sets of brackets to add/change data attributes: `G.edges[1, 2]['weight'] = 4` (For multigraphs: `MG.edges[u, v, key][name] = value`). **Shortcuts:** Many common graph features allow python syntax to speed reporting. >>> 1 in G # check if node in graph True >>> [n for n in G if n < 3] # iterate through nodes [1, 2] >>> len(G) # number of nodes in graph 5 >>> G[1] # adjacency dict-like view keyed by neighbor to edge attributes AdjacencyView({2: {0: {'weight': 4}, 1: {'color': 'blue'}}}) Often the best way to traverse all edges of a graph is via the neighbors. The neighbors are reported as an adjacency-dict `G.adj` or `G.adjacency()`. >>> for n, nbrsdict in G.adjacency(): ... for nbr, keydict in nbrsdict.items(): ... for key, eattr in keydict.items(): ... if "weight" in eattr: ... # Do something useful with the edges ... pass But the edges() method is often more convenient: >>> for u, v, keys, weight in G.edges(data="weight", keys=True): ... if weight is not None: ... # Do something useful with the edges ... pass **Reporting:** Simple graph information is obtained using methods and object-attributes. Reporting usually provides views instead of containers to reduce memory usage. The views update as the graph is updated similarly to dict-views. The objects `nodes, `edges` and `adj` provide access to data attributes via lookup (e.g. `nodes[n], `edges[u, v]`, `adj[u][v]`) and iteration (e.g. `nodes.items()`, `nodes.data('color')`, `nodes.data('color', default='blue')` and similarly for `edges`) Views exist for `nodes`, `edges`, `neighbors()`/`adj` and `degree`. For details on these and other miscellaneous methods, see below. **Subclasses (Advanced):** The MultiGraph class uses a dict-of-dict-of-dict-of-dict data structure. The outer dict (node_dict) holds adjacency information keyed by node. The next dict (adjlist_dict) represents the adjacency information and holds edge_key dicts keyed by neighbor. The edge_key dict holds each edge_attr dict keyed by edge key. The inner dict (edge_attr_dict) represents the edge data and holds edge attribute values keyed by attribute names. Each of these four dicts in the dict-of-dict-of-dict-of-dict structure can be replaced by a user defined dict-like object. In general, the dict-like features should be maintained but extra features can be added. To replace one of the dicts create a new graph class by changing the class(!) variable holding the factory for that dict-like structure. The variable names are node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory, adjlist_outer_dict_factory, edge_key_dict_factory, edge_attr_dict_factory and graph_attr_dict_factory. node_dict_factory : function, (default: dict) Factory function to be used to create the dict containing node attributes, keyed by node id. It should require no arguments and return a dict-like object node_attr_dict_factory: function, (default: dict) Factory function to be used to create the node attribute dict which holds attribute values keyed by attribute name. It should require no arguments and return a dict-like object adjlist_outer_dict_factory : function, (default: dict) Factory function to be used to create the outer-most dict in the data structure that holds adjacency info keyed by node. It should require no arguments and return a dict-like object. adjlist_inner_dict_factory : function, (default: dict) Factory function to be used to create the adjacency list dict which holds multiedge key dicts keyed by neighbor. It should require no arguments and return a dict-like object. edge_key_dict_factory : function, (default: dict) Factory function to be used to create the edge key dict which holds edge data keyed by edge key. It should require no arguments and return a dict-like object. edge_attr_dict_factory : function, (default: dict) Factory function to be used to create the edge attribute dict which holds attribute values keyed by attribute name. It should require no arguments and return a dict-like object. graph_attr_dict_factory : function, (default: dict) Factory function to be used to create the graph attribute dict which holds attribute values keyed by attribute name. It should require no arguments and return a dict-like object. Typically, if your extension doesn't impact the data structure all methods will inherited without issue except: `to_directed/to_undirected`. By default these methods create a DiGraph/Graph class and you probably want them to create your extension of a DiGraph/Graph. To facilitate this we define two class variables that you can set in your subclass. to_directed_class : callable, (default: DiGraph or MultiDiGraph) Class to create a new graph structure in the `to_directed` method. If `None`, a NetworkX class (DiGraph or MultiDiGraph) is used. to_undirected_class : callable, (default: Graph or MultiGraph) Class to create a new graph structure in the `to_undirected` method. If `None`, a NetworkX class (Graph or MultiGraph) is used. Examples -------- Please see :mod:`~networkx.classes.ordered` for examples of creating graph subclasses by overwriting the base class `dict` with a dictionary-like object. """ # node_dict_factory = dict # already assigned in Graph # adjlist_outer_dict_factory = dict # adjlist_inner_dict_factory = dict edge_key_dict_factory = dict # edge_attr_dict_factory = dict def to_directed_class(self): """Returns the class to use for empty directed copies. If you subclass the base classes, use this to designate what directed class to use for `to_directed()` copies. """ return nx.MultiDiGraph def to_undirected_class(self): """Returns the class to use for empty undirected copies. If you subclass the base classes, use this to designate what directed class to use for `to_directed()` copies. """ return MultiGraph
[docs] def __init__(self, incoming_graph_data=None, **attr): """Initialize a graph with edges, name, or graph attributes. Parameters ---------- incoming_graph_data : input graph Data to initialize graph. If incoming_graph_data=None (default) an empty graph is created. The data can be an edge list, or any NetworkX graph object. If the corresponding optional Python packages are installed the data can also be a NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to graph as key=value pairs. See Also -------- convert Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G = nx.Graph(name="my graph") >>> e = [(1, 2), (2, 3), (3, 4)] # list of edges >>> G = nx.Graph(e) Arbitrary graph attribute pairs (key=value) may be assigned >>> G = nx.Graph(e, day="Friday") >>> G.graph {'day': 'Friday'} """ self.edge_key_dict_factory = self.edge_key_dict_factory Graph.__init__(self, incoming_graph_data, **attr)
@property def adj(self): """Graph adjacency object holding the neighbors of each node. This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edgekey-data-dict. So `G.adj[3][2][0]['color'] = 'blue'` sets the color of the edge `(3, 2, 0)` to `"blue"`. Iterating over G.adj behaves like a dict. Useful idioms include `for nbr, nbrdict in G.adj[n].items():`. The neighbor information is also provided by subscripting the graph. So `for nbr, foovalue in G[node].data('foo', default=1):` works. For directed graphs, `G.adj` holds outgoing (successor) info. """ return MultiAdjacencyView(self._adj)
[docs] def new_edge_key(self, u, v): """Returns an unused key for edges between nodes `u` and `v`. The nodes `u` and `v` do not need to be already in the graph. Notes ----- In the standard MultiGraph class the new key is the number of existing edges between `u` and `v` (increased if necessary to ensure unused). The first edge will have key 0, then 1, etc. If an edge is removed further new_edge_keys may not be in this order. Parameters ---------- u, v : nodes Returns ------- key : int """ try: keydict = self._adj[u][v] except KeyError: return 0 key = len(keydict) while key in keydict: key += 1 return key
[docs] def add_edge(self, u_for_edge, v_for_edge, key=None, **attr): """Add an edge between u and v. The nodes u and v will be automatically added if they are not already in the graph. Edge attributes can be specified with keywords or by directly accessing the edge's attribute dictionary. See examples below. Parameters ---------- u_for_edge, v_for_edge : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. key : hashable identifier, optional (default=lowest unused integer) Used to distinguish multiedges between a pair of nodes. attr : keyword arguments, optional Edge data (or labels or objects) can be assigned using keyword arguments. Returns ------- The edge key assigned to the edge. See Also -------- add_edges_from : add a collection of edges Notes ----- To replace/update edge data, use the optional key argument to identify a unique edge. Otherwise a new edge will be created. NetworkX algorithms designed for weighted graphs cannot use multigraphs directly because it is not clear how to handle multiedge weights. Convert to Graph using edge attribute 'weight' to enable weighted graph algorithms. Default keys are generated using the method `new_edge_key()`. This method can be overridden by subclassing the base class and providing a custom `new_edge_key()` method. Examples -------- The following all add the edge e=(1, 2) to graph G: >>> G = nx.MultiGraph() >>> e = (1, 2) >>> ekey = G.add_edge(1, 2) # explicit two-node form >>> G.add_edge(*e) # single edge as tuple of two nodes 1 >>> G.add_edges_from([(1, 2)]) # add edges from iterable container [2] Associate data to edges using keywords: >>> ekey = G.add_edge(1, 2, weight=3) >>> ekey = G.add_edge(1, 2, key=0, weight=4) # update data for key=0 >>> ekey = G.add_edge(1, 3, weight=7, capacity=15, length=342.7) For non-string attribute keys, use subscript notation. >>> ekey = G.add_edge(1, 2) >>> G[1][2][0].update({0: 5}) >>> G.edges[1, 2, 0].update({0: 5}) """ u, v = u_for_edge, v_for_edge # add nodes if u not in self._adj: self._adj[u] = self.adjlist_inner_dict_factory() self._node[u] = self.node_attr_dict_factory() if v not in self._adj: self._adj[v] = self.adjlist_inner_dict_factory() self._node[v] = self.node_attr_dict_factory() if key is None: key = self.new_edge_key(u, v) if v in self._adj[u]: keydict = self._adj[u][v] datadict = keydict.get(key, self.edge_attr_dict_factory()) datadict.update(attr) keydict[key] = datadict else: # selfloops work this way without special treatment datadict = self.edge_attr_dict_factory() datadict.update(attr) keydict = self.edge_key_dict_factory() keydict[key] = datadict self._adj[u][v] = keydict self._adj[v][u] = keydict return key
[docs] def add_edges_from(self, ebunch_to_add, **attr): """Add all the edges in ebunch_to_add. Parameters ---------- ebunch_to_add : container of edges Each edge given in the container will be added to the graph. The edges can be: - 2-tuples (u, v) or - 3-tuples (u, v, d) for an edge data dict d, or - 3-tuples (u, v, k) for not iterable key k, or - 4-tuples (u, v, k, d) for an edge with data and key k attr : keyword arguments, optional Edge data (or labels or objects) can be assigned using keyword arguments. Returns ------- A list of edge keys assigned to the edges in `ebunch`. See Also -------- add_edge : add a single edge add_weighted_edges_from : convenient way to add weighted edges Notes ----- Adding the same edge twice has no effect but any edge data will be updated when each duplicate edge is added. Edge attributes specified in an ebunch take precedence over attributes specified via keyword arguments. Default keys are generated using the method ``new_edge_key()``. This method can be overridden by subclassing the base class and providing a custom ``new_edge_key()`` method. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edges_from([(0, 1), (1, 2)]) # using a list of edge tuples >>> e = zip(range(0, 3), range(1, 4)) >>> G.add_edges_from(e) # Add the path graph 0-1-2-3 Associate data to edges >>> G.add_edges_from([(1, 2), (2, 3)], weight=3) >>> G.add_edges_from([(3, 4), (1, 4)], label="WN2898") """ keylist = [] for e in ebunch_to_add: ne = len(e) if ne == 4: u, v, key, dd = e elif ne == 3: u, v, dd = e key = None elif ne == 2: u, v = e dd = {} key = None else: msg = f"Edge tuple {e} must be a 2-tuple, 3-tuple or 4-tuple." raise NetworkXError(msg) ddd = {} ddd.update(attr) try: ddd.update(dd) except (TypeError, ValueError): if ne != 3: raise key = dd # ne == 3 with 3rd value not dict, must be a key key = self.add_edge(u, v, key) self[u][v][key].update(ddd) keylist.append(key) return keylist
[docs] def remove_edge(self, u, v, key=None): """Remove an edge between u and v. Parameters ---------- u, v : nodes Remove an edge between nodes u and v. key : hashable identifier, optional (default=None) Used to distinguish multiple edges between a pair of nodes. If None remove a single (arbitrary) edge between u and v. Raises ------ NetworkXError If there is not an edge between u and v, or if there is no edge with the specified key. See Also -------- remove_edges_from : remove a collection of edges Examples -------- >>> G = nx.MultiGraph() >>> nx.add_path(G, [0, 1, 2, 3]) >>> G.remove_edge(0, 1) >>> e = (1, 2) >>> G.remove_edge(*e) # unpacks e from an edge tuple For multiple edges >>> G = nx.MultiGraph() # or MultiDiGraph, etc >>> G.add_edges_from([(1, 2), (1, 2), (1, 2)]) # key_list returned [0, 1, 2] >>> G.remove_edge(1, 2) # remove a single (arbitrary) edge For edges with keys >>> G = nx.MultiGraph() # or MultiDiGraph, etc >>> G.add_edge(1, 2, key="first") 'first' >>> G.add_edge(1, 2, key="second") 'second' >>> G.remove_edge(1, 2, key="second") """ try: d = self._adj[u][v] except KeyError as e: raise NetworkXError(f"The edge {u}-{v} is not in the graph.") from e # remove the edge with specified data if key is None: d.popitem() else: try: del d[key] except KeyError as e: msg = f"The edge {u}-{v} with key {key} is not in the graph." raise NetworkXError(msg) from e if len(d) == 0: # remove the key entries if last edge del self._adj[u][v] if u != v: # check for selfloop del self._adj[v][u]
[docs] def remove_edges_from(self, ebunch): """Remove all edges specified in ebunch. Parameters ---------- ebunch: list or container of edge tuples Each edge given in the list or container will be removed from the graph. The edges can be: - 2-tuples (u, v) All edges between u and v are removed. - 3-tuples (u, v, key) The edge identified by key is removed. - 4-tuples (u, v, key, data) where data is ignored. See Also -------- remove_edge : remove a single edge Notes ----- Will fail silently if an edge in ebunch is not in the graph. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> ebunch = [(1, 2), (2, 3)] >>> G.remove_edges_from(ebunch) Removing multiple copies of edges >>> G = nx.MultiGraph() >>> keys = G.add_edges_from([(1, 2), (1, 2), (1, 2)]) >>> G.remove_edges_from([(1, 2), (1, 2)]) >>> list(G.edges()) [(1, 2)] >>> G.remove_edges_from([(1, 2), (1, 2)]) # silently ignore extra copy >>> list(G.edges) # now empty graph [] """ for e in ebunch: try: self.remove_edge(*e[:3]) except NetworkXError: pass
[docs] def has_edge(self, u, v, key=None): """Returns True if the graph has an edge between nodes u and v. This is the same as `v in G[u] or key in G[u][v]` without KeyError exceptions. Parameters ---------- u, v : nodes Nodes can be, for example, strings or numbers. key : hashable identifier, optional (default=None) If specified return True only if the edge with key is found. Returns ------- edge_ind : bool True if edge is in the graph, False otherwise. Examples -------- Can be called either using two nodes u, v, an edge tuple (u, v), or an edge tuple (u, v, key). >>> G = nx.MultiGraph() # or MultiDiGraph >>> nx.add_path(G, [0, 1, 2, 3]) >>> G.has_edge(0, 1) # using two nodes True >>> e = (0, 1) >>> G.has_edge(*e) # e is a 2-tuple (u, v) True >>> G.add_edge(0, 1, key="a") 'a' >>> G.has_edge(0, 1, key="a") # specify key True >>> e = (0, 1, "a") >>> G.has_edge(*e) # e is a 3-tuple (u, v, 'a') True The following syntax are equivalent: >>> G.has_edge(0, 1) True >>> 1 in G[0] # though this gives :exc:`KeyError` if 0 not in G True """ try: if key is None: return v in self._adj[u] else: return key in self._adj[u][v] except KeyError: return False
@property def edges(self): """Returns an iterator over the edges. edges(self, nbunch=None, data=False, keys=False, default=None) The EdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, `G.edges[u, v]['color']` provides the value of the color attribute for edge `(u, v)` while `for (u, v, c) in G.edges(data='color', default='red'):` iterates through all the edges yielding the color attribute. Edges are returned as tuples with optional data and keys in the order (node, neighbor, key, data). Parameters ---------- nbunch : single node, container, or all nodes (default= all nodes) The view will only report edges incident to these nodes. data : string or bool, optional (default=False) The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v). keys : bool, optional (default=False) If True, return edge keys with each edge. default : value, optional (default=None) Value used for edges that don't have the requested attribute. Only relevant if data is not True or False. Returns ------- edges : MultiEdgeView A view of edge attributes, usually it iterates over (u, v) (u, v, k) or (u, v, k, d) tuples of edges, but can also be used for attribute lookup as `edges[u, v, k]['foo']`. Notes ----- Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges. Examples -------- >>> G = nx.MultiGraph() # or MultiDiGraph >>> nx.add_path(G, [0, 1, 2]) >>> key = G.add_edge(2, 3, weight=5) >>> [e for e in G.edges()] [(0, 1), (1, 2), (2, 3)] >>> G.edges.data() # default data is {} (empty dict) MultiEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]) >>> G.edges.data("weight", default=1) MultiEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)]) >>> G.edges(keys=True) # default keys are integers MultiEdgeView([(0, 1, 0), (1, 2, 0), (2, 3, 0)]) >>> G.edges.data(keys=True) MultiEdgeDataView([(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {'weight': 5})]) >>> G.edges.data("weight", default=1, keys=True) MultiEdgeDataView([(0, 1, 0, 1), (1, 2, 0, 1), (2, 3, 0, 5)]) >>> G.edges([0, 3]) MultiEdgeDataView([(0, 1), (3, 2)]) >>> G.edges(0) MultiEdgeDataView([(0, 1)]) """ return MultiEdgeView(self)
[docs] def get_edge_data(self, u, v, key=None, default=None): """Returns the attribute dictionary associated with edge (u, v). This is identical to `G[u][v][key]` except the default is returned instead of an exception is the edge doesn't exist. Parameters ---------- u, v : nodes default : any Python object (default=None) Value to return if the edge (u, v) is not found. key : hashable identifier, optional (default=None) Return data only for the edge with specified key. Returns ------- edge_dict : dictionary The edge attribute dictionary. Examples -------- >>> G = nx.MultiGraph() # or MultiDiGraph >>> key = G.add_edge(0, 1, key="a", weight=7) >>> G[0][1]["a"] # key='a' {'weight': 7} >>> G.edges[0, 1, "a"] # key='a' {'weight': 7} Warning: we protect the graph data structure by making `G.edges` and `G[1][2]` read-only dict-like structures. However, you can assign values to attributes in e.g. `G.edges[1, 2, 'a']` or `G[1][2]['a']` using an additional bracket as shown next. You need to specify all edge info to assign to the edge data associated with an edge. >>> G[0][1]["a"]["weight"] = 10 >>> G.edges[0, 1, "a"]["weight"] = 10 >>> G[0][1]["a"]["weight"] 10 >>> G.edges[1, 0, "a"]["weight"] 10 >>> G = nx.MultiGraph() # or MultiDiGraph >>> nx.add_path(G, [0, 1, 2, 3]) >>> G.get_edge_data(0, 1) {0: {}} >>> e = (0, 1) >>> G.get_edge_data(*e) # tuple form {0: {}} >>> G.get_edge_data("a", "b", default=0) # edge not in graph, return 0 0 """ try: if key is None: return self._adj[u][v] else: return self._adj[u][v][key] except KeyError: return default
@property def degree(self): """A DegreeView for the Graph as G.degree or G.degree(). The node degree is the number of edges adjacent to the node. The weighted node degree is the sum of the edge weights for edges incident to that node. This object provides an iterator for (node, degree) as well as lookup for the degree for a single node. Parameters ---------- nbunch : single node, container, or all nodes (default= all nodes) The view will only report edges incident to these nodes. weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. Returns ------- If a single node is requested deg : int Degree of the node, if a single node is passed as argument. OR if multiple nodes are requested nd_iter : iterator The iterator returns two-tuples of (node, degree). Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> nx.add_path(G, [0, 1, 2, 3]) >>> G.degree(0) # node 0 with degree 1 1 >>> list(G.degree([0, 1])) [(0, 1), (1, 2)] """ return MultiDegreeView(self) def is_multigraph(self): """Returns True if graph is a multigraph, False otherwise.""" return True def is_directed(self): """Returns True if graph is directed, False otherwise.""" return False
[docs] def copy(self, as_view=False): """Returns a copy of the graph. The copy method by default returns an independent shallow copy of the graph and attributes. That is, if an attribute is a container, that container is shared by the original an the copy. Use Python's `copy.deepcopy` for new containers. If `as_view` is True then a view is returned instead of a copy. Notes ----- All copies reproduce the graph structure, but data attributes may be handled in different ways. There are four types of copies of a graph that people might want. Deepcopy -- A "deepcopy" copies the graph structure as well as all data attributes and any objects they might contain. The entire graph object is new so that changes in the copy do not affect the original object. (see Python's copy.deepcopy) Data Reference (Shallow) -- For a shallow copy the graph structure is copied but the edge, node and graph attribute dicts are references to those in the original graph. This saves time and memory but could cause confusion if you change an attribute in one graph and it changes the attribute in the other. NetworkX does not provide this level of shallow copy. Independent Shallow -- This copy creates new independent attribute dicts and then does a shallow copy of the attributes. That is, any attributes that are containers are shared between the new graph and the original. This is exactly what `dict.copy()` provides. You can obtain this style copy using: >>> G = nx.path_graph(5) >>> H = G.copy() >>> H = G.copy(as_view=False) >>> H = nx.Graph(G) >>> H = G.__class__(G) Fresh Data -- For fresh data, the graph structure is copied while new empty data attribute dicts are created. The resulting graph is independent of the original and it has no edge, node or graph attributes. Fresh copies are not enabled. Instead use: >>> H = G.__class__() >>> H.add_nodes_from(G) >>> H.add_edges_from(G.edges) View -- Inspired by dict-views, graph-views act like read-only versions of the original graph, providing a copy of the original structure without requiring any memory for copying the information. See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html. Parameters ---------- as_view : bool, optional (default=False) If True, the returned graph-view provides a read-only view of the original graph without actually copying any data. Returns ------- G : Graph A copy of the graph. See Also -------- to_directed: return a directed copy of the graph. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> H = G.copy() """ if as_view is True: return nx.graphviews.generic_graph_view(self) G = self.__class__() G.graph.update(self.graph) G.add_nodes_from((n, d.copy()) for n, d in self._node.items()) G.add_edges_from( (u, v, key, datadict.copy()) for u, nbrs in self._adj.items() for v, keydict in nbrs.items() for key, datadict in keydict.items() ) return G
[docs] def to_directed(self, as_view=False): """Returns a directed representation of the graph. Returns ------- G : MultiDiGraph A directed graph with the same name, same nodes, and with each edge (u, v, data) replaced by two directed edges (u, v, data) and (v, u, data). Notes ----- This returns a "deepcopy" of the edge, node, and graph attributes which attempts to completely copy all of the data and references. This is in contrast to the similar D=DiGraph(G) which returns a shallow copy of the data. See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html. Warning: If you have subclassed MultiGraph to use dict-like objects in the data structure, those changes do not transfer to the MultiDiGraph created by this method. Examples -------- >>> G = nx.Graph() # or MultiGraph, etc >>> G.add_edge(0, 1) >>> H = G.to_directed() >>> list(H.edges) [(0, 1), (1, 0)] If already directed, return a (deep) copy >>> G = nx.DiGraph() # or MultiDiGraph, etc >>> G.add_edge(0, 1) >>> H = G.to_directed() >>> list(H.edges) [(0, 1)] """ graph_class = self.to_directed_class() if as_view is True: return nx.graphviews.generic_graph_view(self, graph_class) # deepcopy when not a view G = graph_class() G.graph.update(deepcopy(self.graph)) G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items()) G.add_edges_from( (u, v, key, deepcopy(datadict)) for u, nbrs in self.adj.items() for v, keydict in nbrs.items() for key, datadict in keydict.items() ) return G
[docs] def to_undirected(self, as_view=False): """Returns an undirected copy of the graph. Returns ------- G : Graph/MultiGraph A deepcopy of the graph. See Also -------- copy, add_edge, add_edges_from Notes ----- This returns a "deepcopy" of the edge, node, and graph attributes which attempts to completely copy all of the data and references. This is in contrast to the similar `G = nx.MultiGraph(D)` which returns a shallow copy of the data. See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html. Warning: If you have subclassed MultiiGraph to use dict-like objects in the data structure, those changes do not transfer to the MultiGraph created by this method. Examples -------- >>> G = nx.path_graph(2) # or MultiGraph, etc >>> H = G.to_directed() >>> list(H.edges) [(0, 1), (1, 0)] >>> G2 = H.to_undirected() >>> list(G2.edges) [(0, 1)] """ graph_class = self.to_undirected_class() if as_view is True: return nx.graphviews.generic_graph_view(self, graph_class) # deepcopy when not a view G = graph_class() G.graph.update(deepcopy(self.graph)) G.add_nodes_from((n, deepcopy(d)) for n, d in self._node.items()) G.add_edges_from( (u, v, key, deepcopy(datadict)) for u, nbrs in self._adj.items() for v, keydict in nbrs.items() for key, datadict in keydict.items() ) return G
[docs] def number_of_edges(self, u=None, v=None): """Returns the number of edges between two nodes. Parameters ---------- u, v : nodes, optional (Gefault=all edges) If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges. Returns ------- nedges : int The number of edges in the graph. If nodes `u` and `v` are specified return the number of edges between those nodes. If the graph is directed, this only returns the number of edges from `u` to `v`. See Also -------- size Examples -------- For undirected multigraphs, this method counts the total number of edges in the graph:: >>> G = nx.MultiGraph() >>> G.add_edges_from([(0, 1), (0, 1), (1, 2)]) [0, 1, 0] >>> G.number_of_edges() 3 If you specify two nodes, this counts the total number of edges joining the two nodes:: >>> G.number_of_edges(0, 1) 2 For directed multigraphs, this method can count the total number of directed edges from `u` to `v`:: >>> G = nx.MultiDiGraph() >>> G.add_edges_from([(0, 1), (0, 1), (1, 0)]) [0, 1, 0] >>> G.number_of_edges(0, 1) 2 >>> G.number_of_edges(1, 0) 1 """ if u is None: return self.size() try: edgedata = self._adj[u][v] except KeyError: return 0 # no such edge return len(edgedata)