hSrSSKJr SSKJr SSKrSSKJr SSKJ r SSK J r J r J r SSKJr S /r"S S 5r"S S 5r"SS 5rg)aBase class for undirected graphs. The Graph class allows any hashable object as a node and can associate key/value attribute pairs with each undirected edge. Self-loops are allowed but multiple edges are not (see MultiGraph). For directed graphs see DiGraph and MultiDiGraph. deepcopy)cached_propertyN)convert) AdjacencyView) DegreeViewEdgeViewNodeView) NetworkXErrorGraphc\rSrSrSrSrSrg)_CachedPropertyResetterAdja4Data Descriptor class for _adj that resets ``adj`` cached_property when needed This assumes that the ``cached_property`` ``G.adj`` should be reset whenever ``G._adj`` is set to a new value. This object sits on a class and ensures that any instance of that class clears its cached property "adj" whenever the underlying instance attribute "_adj" is set to a new object. It only affects the set process of the obj._adj attribute. All get/del operations act as they normally would. For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html cPURnX#S'/SQnUH nXS;dM X5 M g)N_adj)adjedgesdegree__dict__)selfobjvalueodpropsprops H/var/www/html/env/lib/python3.13/site-packages/networkx/classes/graph.py__set__"_CachedPropertyResetterAdj.__set__&s+ \\6 *DzHN__name__ __module__ __qualname____firstlineno____doc__r__static_attributes__r!r rrrs  r rc\rSrSrSrSrSrg)_CachedPropertyResetterNode0a<Data Descriptor class for _node that resets ``nodes`` cached_property when needed This assumes that the ``cached_property`` ``G.node`` should be reset whenever ``G._node`` is set to a new value. This object sits on a class and ensures that any instance of that class clears its cached property "nodes" whenever the underlying instance attribute "_node" is set to a new object. It only affects the set process of the obj._adj attribute. All get/del operations act as they normally would. For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html c8URnX#S'SU;aUS gg)N_nodenodesr)rrrrs rr#_CachedPropertyResetterNode.__set__?s% \\7 b=7  r r!Nr"r!r rr*r*0s  r r*c\rSrSrSrSr\"5r\"5r \ r \ r \ r \ r\ r\ rSrSrS1Sjr\S5r\S 5r\R0S 5rS rS rS rSrSrSrSrSr Sr!\S5r"Sr#Sr$Sr%Sr&Sr'S2Sjr(Sr)Sr*S3Sjr+Sr,Sr-\S 5r.S1S!jr/S"r0\S#5r1S$r2S%r3S&r4S'r5S4S(jr6S4S)jr7S4S*jr8S+r9S,r:S1S-jr;S3S.jrg)5r Ga Base class for undirected graphs. A Graph stores nodes and edges with optional data, or attributes. Graphs hold undirected edges. Self loops are allowed but multiple (parallel) edges are not. Nodes can be arbitrary (hashable) Python objects with optional key/value attributes, except that `None` is not allowed 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, 2D NumPy array, SciPy sparse matrix, or PyGraphviz graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to graph as key=value pairs. See Also -------- DiGraph MultiGraph MultiDiGraph Examples -------- Create an empty graph structure (a "null graph") with no nodes and no edges. >>> G = nx.Graph() 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, >>> G.add_edge(1, 2) a list of edges, >>> G.add_edges_from([(1, 2), (1, 3)]) or a collection of edges, >>> G.add_edges_from(H.edges) If some edges connect nodes not yet in the graph, the nodes are added automatically. There are no errors when adding nodes or edges that already exist. **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.Graph(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 # node must exist already to use G.nodes >>> 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. >>> G.add_edge(1, 2, weight=4.7) >>> G.add_edges_from([(3, 4), (4, 5)], color="red") >>> G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})]) >>> G[1][2]["weight"] = 4.7 >>> G.edges[1, 2]["weight"] = 4 Warning: we protect the graph data structure by making `G.edges` 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 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, eattr in nbrsdict.items(): ... if "weight" in eattr: ... # Do something useful with the edges ... pass But the edges() method is often more convenient: >>> for u, v, weight in G.edges.data("weight"): ... if weight is not None: ... # Do something useful with the edges ... pass **Reporting:** Simple graph information is obtained using object-attributes and methods. Reporting typically 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 Graph class uses a 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 data keyed by neighbor. The inner dict (edge_attr_dict) represents the edge data and holds edge attribute values keyed by attribute names. Each of these three dicts can be replaced in a subclass 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. 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 edge data keyed by neighbor. 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 inherit 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. **Subclassing Example** Create a low memory graph class that effectively disallows edge attributes by using a single attribute dict for all edges. This reduces the memory used, but you lose edge attributes. >>> class ThinGraph(nx.Graph): ... all_edge_dict = {"weight": 1} ... ... def single_edge_dict(self): ... return self.all_edge_dict ... ... edge_attr_dict_factory = single_edge_dict >>> G = ThinGraph() >>> G.add_edge(2, 1) >>> G[2][1] {'weight': 1} >>> G.add_edge(2, 2) >>> G[2][1] is G[2][2] True networkxc"[R$)zReturns the class to use for empty directed copies. If you subclass the base classes, use this to designate what directed class to use for `to_directed()` copies. )nxDiGraphrs rto_directed_classGraph.to_directed_classCs zzr c[$)zReturns 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. )r r6s rto_undirected_classGraph.to_undirected_classKs  r Nc UR5UlUR5UlUR 5Ul0UlUb[R"XS9 URRU5 g)a{Initialize a graph with edges, name, or graph 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 an edge list, or any NetworkX graph object. If the corresponding optional Python packages are installed the data can also be a 2D NumPy array, a SciPy sparse array, 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'} N) create_using) graph_attr_dict_factorygraphnode_dict_factoryr-adjlist_outer_dict_factoryr__networkx_cache__rto_networkx_graphupdate)rincoming_graph_dataattrs r__init__Graph.__init__SsdB113 ++- 335 "$  *  % %&9 M $r c,[UR5$)aYGraph 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 edge-data-dict. So `G.adj[3][2]['color'] = 'blue'` sets the color of the edge `(3, 2)` to `"blue"`. Iterating over G.adj behaves like a dict. Useful idioms include `for nbr, datadict 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. )rrr6s rr Graph.adj~s"TYY''r c:URRSS5$)zString identifier of the graph. This graph attribute appears in the attribute dict G.graph keyed by the string `"name"`. as well as an attribute (technically a property) `G.name`. This is entirely user controlled. name)r?getr6s rrL Graph.nameszz~~fb))r cLXRS'[R"U5 g)NrL)r?r4 _clear_cache)rss rrLrOs 6 r c SR[U5RUR(aSUR<3OSSUR 5SUR 5S3/5$)a`Returns a short summary of the graph. Returns ------- info : string Graph information including the graph name (if any), graph type, and the number of nodes and edges. Examples -------- >>> G = nx.Graph(name="foo") >>> str(G) "Graph named 'foo' with 0 nodes and 0 edges" >>> G = nx.path_graph(3) >>> str(G) 'Graph with 3 nodes and 2 edges' rMz named z with z nodes and z edges)jointyper#rLnumber_of_nodesnumber_of_edgesr6s r__str__ Graph.__str__sd(wwT ##+/99'$))'"--/0 D>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> [n for n in G] [0, 1, 2, 3] >>> list(G) [0, 1, 2, 3] )iterr-r6s r__iter__Graph.__iter__s DJJr c@XR;$![a gf=f)zReturns True if n is a node, False otherwise. Use: 'n in G'. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> 1 in G True Fr- TypeErrorrns r __contains__Graph.__contains__s%  ? "    c,[UR5$)a1Returns the number of nodes in the graph. Use: 'len(G)'. Returns ------- nnodes : int The number of nodes in the graph. See Also -------- number_of_nodes: identical method order: identical method Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> len(G) 4 lenr-r6s r__len__ Graph.__len__s(4::r c URU$)aReturns a dict of neighbors of node n. Use: 'G[n]'. Parameters ---------- n : node A node in the graph. Returns ------- adj_dict : dictionary The adjacency dictionary for nodes connected to n. Notes ----- G[n] is the same as G.adj[n] and similar to G.neighbors(n) (which is an iterator over G.adj[n]) Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G[0] AtlasView({1: {}}) )rras r __getitem__Graph.__getitem__s0xx{r c @XR;a[Uc [S5eUR5URU'UR 5=o0RU'UR U5 OURUR U5 [ R"U5 g)aAdd a single node `node_for_adding` and update node attributes. Parameters ---------- node_for_adding : node A node can be any hashable Python object except None. attr : keyword arguments, optional Set or change node attributes using key=value. See Also -------- add_nodes_from Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_node(1) >>> G.add_node("Hello") >>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)]) >>> G.add_node(K3) >>> G.number_of_nodes() 3 Use keywords set/change node attributes: >>> G.add_node(1, size=10) >>> G.add_node(3, weight=0.4, UTM=("13S", 382871, 3972649)) Notes ----- A hashable object is one that can be used as a key in a Python dictionary. This includes strings, numbers, tuples of strings and numbers, etc. On many platforms hashable items also include mutables such as NetworkX Graphs, though one should be careful that the hash doesn't change on mutables. NNone cannot be a node)r- ValueErroradjlist_inner_dict_factoryrnode_attr_dict_factoryrDr4rQ)rnode_for_addingrF attr_dicts radd_nodeGraph.add_node sN ** ,& !899)-)H)H)JDIIo &6:6Q6Q6S SI ?3   T " JJ ' . .t 4 r c UHnX0R;nUnU(aHUc [ S5eUR 5UR U'UR5URU'URURU5 M [R"U5 g![a6 Uup6X0R;nUR5nURU5 Nf=f)a%Add multiple nodes. Parameters ---------- nodes_for_adding : iterable container A container of nodes (list, dict, set, etc.). OR A container of (node, attribute dict) tuples. Node attributes are updated using the attribute dict. attr : keyword arguments, optional (default= no attributes) Update attributes for all nodes in nodes. Node attributes specified in nodes as a tuple take precedence over attributes specified via keyword arguments. See Also -------- add_node Notes ----- When adding nodes from an iterator over the graph you are changing, a `RuntimeError` can be raised with message: `RuntimeError: dictionary changed size during iteration`. This happens when the graph's underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using `list(iterator_of_nodes)`, and pass this object to `G.add_nodes_from`. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_nodes_from("Hello") >>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)]) >>> G.add_nodes_from(K3) >>> sorted(G.nodes(), key=str) [0, 1, 2, 'H', 'e', 'l', 'o'] Use keywords to update specific node attributes for every node. >>> G.add_nodes_from([1, 2], size=10) >>> G.add_nodes_from([3, 4], weight=0.4) Use (node, attrdict) tuples to update attributes for specific nodes. >>> G.add_nodes_from([(1, dict(size=11)), (2, {"color": "blue"})]) >>> G.nodes[1]["size"] 11 >>> H = nx.Graph() >>> H.add_nodes_from(G.nodes(data=True)) >>> H.nodes[1]["size"] 11 Evaluate an iterator over a graph if using it to modify the same graph >>> G = nx.Graph([(0, 1), (1, 2), (3, 4)]) >>> # wrong way - will raise RuntimeError >>> # G.add_nodes_from(n + 1 for n in G.nodes) >>> # correct way >>> G.add_nodes_from(list(n + 1 for n in G.nodes)) Nro) r-r`copyrDrprqrrrr4rQ)rnodes_for_addingrFrbnewnodenewdictndicts radd_nodes_fromGraph.add_nodes_from=sz"A &::- 9$%<==#>>@ ! $ ; ; = 1 JJqM  )"  &::-))+u%  &sB=CCcURn[X!5nURU UHnX%U M X! [ R "U5 g![an[ SUS35UeSnAff=f)aRemove node n. Removes the node n and all adjacent edges. Attempting to remove a nonexistent node will raise an exception. Parameters ---------- n : node A node in the graph Raises ------ NetworkXError If n is not in the graph. See Also -------- remove_nodes_from Examples -------- >>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> list(G.edges) [(0, 1), (1, 2)] >>> G.remove_node(1) >>> list(G.edges) [] The node  is not in the graph.N)rlistr-KeyErrorr r4rQ)rrbrnbrserrus r remove_nodeGraph.remove_nodesz<ii O>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> e = list(G.nodes) >>> e [0, 1, 2] >>> G.remove_nodes_from(e) >>> list(G.nodes) [] Evaluate an iterator over a graph if using it to modify the same graph >>> G = nx.Graph([(0, 1), (1, 2), (3, 4)]) >>> # this command will fail, as the graph's dict is modified during iteration >>> # G.remove_nodes_from(n for n in G.nodes if n < 2) >>> # this command will work, since the dictionary underlying graph is not modified >>> G.remove_nodes_from(list(n for n in G.nodes if n < 2)) N)rr-rrr4rQ)rr.rrbrs rremove_nodes_fromGraph.remove_nodes_fromshTiiA JJqMcfAq &F    s(A A$#A$c[U5$)a A NodeView of the Graph as G.nodes or G.nodes(). Can be used as `G.nodes` for data lookup and for set-like operations. Can also be used as `G.nodes(data='color', default=None)` to return a NodeDataView which reports specific node data but no set operations. It presents a dict-like interface as well with `G.nodes.items()` iterating over `(node, nodedata)` 2-tuples and `G.nodes[3]['foo']` providing the value of the `foo` attribute for node `3`. In addition, a view `G.nodes.data('foo')` provides a dict-like interface to the `foo` attribute of each node. `G.nodes.data('foo', default=1)` provides a default for nodes that do not have attribute `foo`. Parameters ---------- data : string or bool, optional (default=False) The node attribute returned in 2-tuple (n, ddict[data]). If True, return entire node attribute dict as (n, ddict). If False, return just the nodes n. default : value, optional (default=None) Value used for nodes that don't have the requested attribute. Only relevant if data is not True or False. Returns ------- NodeView Allows set-like operations over the nodes as well as node attribute dict lookup and calling to get a NodeDataView. A NodeDataView iterates over `(n, data)` and has no set operations. A NodeView iterates over `n` and includes set operations. When called, if data is False, an iterator over nodes. Otherwise an iterator of 2-tuples (node, attribute value) where the attribute is specified in `data`. If data is True then the attribute becomes the entire data dictionary. Notes ----- If your node data is not needed, it is simpler and equivalent to use the expression ``for n in G``, or ``list(G)``. Examples -------- There are two simple ways of getting a list of all nodes in the graph: >>> G = nx.path_graph(3) >>> list(G.nodes) [0, 1, 2] >>> list(G) [0, 1, 2] To get the node data along with the nodes: >>> G.add_node(1, time="5pm") >>> G.nodes[0]["foo"] = "bar" >>> list(G.nodes(data=True)) [(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})] >>> list(G.nodes.data()) [(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})] >>> list(G.nodes(data="foo")) [(0, 'bar'), (1, None), (2, None)] >>> list(G.nodes.data("foo")) [(0, 'bar'), (1, None), (2, None)] >>> list(G.nodes(data="time")) [(0, None), (1, '5pm'), (2, None)] >>> list(G.nodes.data("time")) [(0, None), (1, '5pm'), (2, None)] >>> list(G.nodes(data="time", default="Not Available")) [(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')] >>> list(G.nodes.data("time", default="Not Available")) [(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')] If some of your nodes have an attribute and the rest are assumed to have a default attribute value you can create a dictionary from node/attribute pairs using the `default` keyword argument to guarantee the value is never None:: >>> G = nx.Graph() >>> G.add_node(0) >>> G.add_node(1, weight=2) >>> G.add_node(2, weight=3) >>> dict(G.nodes(data="weight", default=1)) {0: 1, 1: 2, 2: 3} )r r6s rr. Graph.nodessv~r c,[UR5$)a&Returns the number of nodes in the graph. Returns ------- nnodes : int The number of nodes in the graph. See Also -------- order: identical method __len__: identical method Examples -------- >>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.number_of_nodes() 3 rgr6s rrVGraph.number_of_nodesF&4::r c,[UR5$)a&Returns the number of nodes in the graph. Returns ------- nnodes : int The number of nodes in the graph. See Also -------- number_of_nodes: identical method __len__: identical method Examples -------- >>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.order() 3 rgr6s rorder Graph.order[rr c@XR;$![a gf=f)aReturns True if the graph contains the node n. Identical to `n in G` Parameters ---------- n : node Examples -------- >>> G = nx.path_graph(3) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.has_node(0) True It is more readable and simpler to use >>> 0 in G True Fr_ras rhas_nodeGraph.has_nodeps%*  ? "  rec NXpTX@R;aHUc [S5eUR5URU'UR 5URU'XPR;aHUc [S5eUR5URU'UR 5URU'URUR XPR 55nURU5 X`RUU'X`RUU'[R"U5 g)aXAdd 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_of_edge, v_of_edge : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. attr : keyword arguments, optional Edge data (or labels or objects) can be assigned using keyword arguments. See Also -------- add_edges_from : add a collection of edges Notes ----- Adding an edge that already exists updates the edge data. Many NetworkX algorithms designed for weighted graphs use an edge attribute (by default `weight`) to hold a numerical value. Examples -------- The following all add the edge e=(1, 2) to graph G: >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> e = (1, 2) >>> G.add_edge(1, 2) # explicit two-node form >>> G.add_edge(*e) # single edge as tuple of two nodes >>> G.add_edges_from([(1, 2)]) # add edges from iterable container Associate data to edges using keywords: >>> G.add_edge(1, 2, weight=3) >>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7) For non-string attribute keys, use subscript notation. >>> G.add_edge(1, 2) >>> G[1][2].update({0: 5}) >>> G.edges[1, 2].update({0: 5}) Nro) r-rprqrrrrNedge_attr_dict_factoryrDr4rQ)r u_of_edge v_of_edgerFrvdatadicts radd_edgeGraph.add_edgesd1 JJ y !899::>> 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") Evaluate an iterator over a graph if using it to modify the same graph >>> G = nx.Graph([(1, 2), (2, 3), (3, 4)]) >>> # Grow graph by one new node, adding edges to all existing nodes. >>> # wrong way - will raise RuntimeError >>> # G.add_edges_from(((5, n) for n in G.nodes)) >>> # correct way - note that there will be no self-edge for node 5 >>> G.add_edges_from(list((5, n) for n in G.nodes)) z Edge tuple z must be a 2-tuple or 3-tuple.Nro) rhr r-rprqrrrrNrrDr4rQ) r ebunch_to_addrFenerrddrs radd_edges_fromGraph.add_edges_fromsCnAQBQwbq#k!4R$STT "9$%<==#>>@ ! $ ; ; = 1  "9$%<==#>>@ ! $ ; ; = 1 yy|''+F+F+HIH OOD ! OOB &IIaLO&IIaLO/0 r c l^UR"U4SjU540UD6 [R"U5 g)aAdd weighted edges in `ebunch_to_add` with specified weight attr Parameters ---------- ebunch_to_add : container of edges Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number. weight : string, optional (default= 'weight') The attribute name for the edge weights to be added. attr : keyword arguments, optional (default= no attributes) Edge attributes to add/update for all edges. See Also -------- add_edge : add a single edge add_edges_from : add multiple edges Notes ----- Adding the same edge twice for Graph/DiGraph simply updates the edge data. For MultiGraph/MultiDiGraph, duplicate edges are stored. When adding edges from an iterator over the graph you are changing, a `RuntimeError` can be raised with message: `RuntimeError: dictionary changed size during iteration`. This happens when the graph's underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using `list(iterator_of_edges)`, and pass this object to `G.add_weighted_edges_from`. Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)]) Evaluate an iterator over edges before passing it >>> G = nx.Graph([(1, 2), (2, 3), (3, 4)]) >>> weight = 0.1 >>> # Grow graph by one new node, adding edges to all existing nodes. >>> # wrong way - will raise RuntimeError >>> # G.add_weighted_edges_from(((5, n, weight) for n in G.nodes)) >>> # correct way - note that there will be no self-edge for node 5 >>> G.add_weighted_edges_from(list((5, n, weight) for n in G.nodes)) c36># UHupo1UTU04v M g7fNr!).0rrdweights r 0Graph.add_weighted_edges_from..PsN WQ1VQK0 sN)rr4rQ)rrrrFs ` radd_weighted_edges_fromGraph.add_weighted_edges_from s,` N NWRVW r cURUU X:waURUU [R"U5 g![an[SUSUS35UeSnAff=f)aRemove the edge between u and v. Parameters ---------- u, v : nodes Remove the edge between nodes u and v. Raises ------ NetworkXError If there is not an edge between u and v. See Also -------- remove_edges_from : remove a collection of edges Examples -------- >>> G = nx.path_graph(4) # or DiGraph, etc >>> G.remove_edge(0, 1) >>> e = (1, 2) >>> G.remove_edge(*e) # unpacks e from an edge tuple >>> e = (2, 3, {"weight": 7}) # an edge with attribute data >>> G.remove_edge(*e[:2]) # select first part of edge tuple z The edge -z is not in the graphN)rrr r4rQ)rrrrs r remove_edgeGraph.remove_edgeSsj4 R ! QvIIaLO  R)A3as2F GHc Q Rs%> A AA cURnUH,nUSSupEXB;dMXRU;dMX$U XE:wdM'X%U M. [R"U5 g)aBRemove 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) edge between u and v. - 3-tuples (u, v, k) where k 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) Nr)rr4rQ)rebunchrrrrs rremove_edges_fromGraph.remove_edges_fromusV4iiARa5DAxAQKF1I6q  r cUbUb#URU5 URU5 gURnURnURUR 55 URUR 55 UR R UR 5 gUbURU5 g[S5e![a URU5 gf=f)aP Update the graph using nodes/edges/graphs as input. Like dict.update, this method takes a graph as input, adding the graph's nodes and edges to this graph. It can also take two inputs: edges and nodes. Finally it can take either edges or nodes. To specify only nodes the keyword `nodes` must be used. The collections of edges and nodes are treated similarly to the add_edges_from/add_nodes_from methods. When iterated, they should yield 2-tuples (u, v) or 3-tuples (u, v, datadict). Parameters ---------- edges : Graph object, collection of edges, or None The first parameter can be a graph or some edges. If it has attributes `nodes` and `edges`, then it is taken to be a Graph-like object and those attributes are used as collections of nodes and edges to be added to the graph. If the first parameter does not have those attributes, it is treated as a collection of edges and added to the graph. If the first argument is None, no edges are added. nodes : collection of nodes, or None The second parameter is treated as a collection of nodes to be added to the graph unless it is None. If `edges is None` and `nodes is None` an exception is raised. If the first parameter is a Graph, then `nodes` is ignored. Examples -------- >>> G = nx.path_graph(5) >>> G.update(nx.complete_graph(range(4, 10))) >>> from itertools import combinations >>> edges = ( ... (u, v, {"power": u * v}) ... for u, v in combinations(range(10, 20), 2) ... if u * v < 225 ... ) >>> nodes = [1000] # for singleton, use a container >>> G.update(edges, nodes) Notes ----- It you want to update the graph using an adjacency structure it is straightforward to obtain the edges/nodes from adjacency. The following examples provide common cases, your adjacency may be slightly different and require tweaks of these examples:: >>> # dict-of-set/list/tuple >>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}} >>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs] >>> G.update(edges=e, nodes=adj) >>> DG = nx.DiGraph() >>> # dict-of-dict-of-attribute >>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}} >>> e = [ ... (u, v, {"weight": d}) ... for u, nbrs in adj.items() ... for v, d in nbrs.items() ... ] >>> DG.update(edges=e, nodes=adj) >>> # dict-of-dict-of-dict >>> adj = {1: {2: {"weight": 1.3}, 3: {"color": 0.7, "weight": 1.2}}} >>> e = [ ... (u, v, {"weight": d}) ... for u, nbrs in adj.items() ... for v, d in nbrs.items() ... ] >>> DG.update(edges=e, nodes=adj) >>> # predecessor adjacency (dict-of-set) >>> pred = {1: {2, 3}, 2: {3}, 3: {3}} >>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs] >>> # MultiGraph dict-of-dict-of-dict-of-attribute >>> MDG = nx.MultiDiGraph() >>> adj = { ... 1: {2: {0: {"weight": 1.3}, 1: {"weight": 1.2}}}, ... 3: {2: {0: {"weight": 0.7}}}, ... } >>> e = [ ... (u, v, ekey, d) ... for u, nbrs in adj.items() ... for v, keydict in nbrs.items() ... for ekey, d in keydict.items() ... ] >>> MDG.update(edges=e) See Also -------- add_edges_from: add multiple edges to a graph add_nodes_from: add multiple nodes to a graph Nz!update needs nodes or edges input) r}rr.rdatar?rDAttributeErrorr )rrr. graph_nodes graph_edgess rrD Graph.updates~   ##E*##E* 3"'++K"'++K '' (8(8(:;'' (8(8(:;JJ%%ekk2      & CD D&/''./sCC%$C%cFX RU;$![a gf=f)aReturns True if the edge (u, v) is in the graph. This is the same as `v in G[u]` without KeyError exceptions. Parameters ---------- u, v : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. Returns ------- edge_ind : bool True if edge is in the graph, False otherwise. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.has_edge(0, 1) # using two nodes True >>> e = (0, 1) >>> G.has_edge(*e) # e is a 2-tuple (u, v) True >>> e = (0, 1, {"weight": 7}) >>> G.has_edge(*e[:2]) # e is a 3-tuple (u, v, data_dictionary) True The following syntax are equivalent: >>> G.has_edge(0, 1) True >>> 1 in G[0] # though this gives KeyError if 0 not in G True Frrrrrs rhas_edgeGraph.has_edge s+H  ! $ $  s   cx[URU5$![an[SUS35UeSnAff=f)aReturns an iterator over all neighbors of node n. This is identical to `iter(G[n])` Parameters ---------- n : node A node in the graph Returns ------- neighbors : iterator An iterator over all neighbors of node n Raises ------ NetworkXError If the node n is not in the graph. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> [n for n in G.neighbors(0)] [1] Notes ----- Alternate ways to access the neighbors are ``G.adj[n]`` or ``G[n]``: >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge("a", "b", weight=7) >>> G["a"] AtlasView({'b': {'weight': 7}}) >>> G = nx.path_graph(4) >>> [n for n in G[0]] [1] rrN)r[rrr )rrbrs r neighborsGraph.neighbors5sEL O ! % % O)A3.C DE3 N Os 949c[U5$)aAn EdgeView of the Graph as G.edges or G.edges(). edges(self, nbunch=None, data=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 with default `'red'` if no color attribute exists. Parameters ---------- nbunch : single node, container, or all nodes (default= all nodes) The view will only report edges from 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). 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 : EdgeView A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as `edges[u, v]['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.path_graph(3) # or MultiGraph, etc >>> 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) EdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})]) >>> G.edges.data("weight", default=1) EdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)]) >>> G.edges([0, 3]) # only edges from these nodes EdgeDataView([(0, 1), (3, 2)]) >>> G.edges(0) # only edges from node 0 EdgeDataView([(0, 1)]) )r r6s rr Graph.edges`sn~r cLURUU$![a Us$f=f)aReturns the attribute dictionary associated with edge (u, v). This is identical to `G[u][v]` except the default is returned instead of an exception if 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. Returns ------- edge_dict : dictionary The edge attribute dictionary. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G[0][1] {} Warning: Assigning to `G[u][v]` is not permitted. But it is safe to assign attributes `G[u][v]['foo']` >>> G[0][1]["weight"] = 7 >>> G[0][1]["weight"] 7 >>> G[1][0]["weight"] 7 >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.get_edge_data(0, 1) # default edge data is {} {} >>> e = (0, 1) >>> G.get_edge_data(*e) # tuple form {} >>> G.get_edge_data("a", "b", default=0) # edge not in graph, return 0 0 r)rrrdefaults r get_edge_dataGraph.get_edge_datas.R 99Q<? " N s  ##cH[URR55$)aReturns an iterator over (node, adjacency dict) tuples for all nodes. For directed graphs, only outgoing neighbors/adjacencies are included. Returns ------- adj_iter : iterator An iterator over (node, adjacency dictionary) for all nodes in the graph. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> [(n, nbrdict) for n, nbrdict in G.adjacency()] [(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})] )r[ritemsr6s r adjacencyGraph.adjacencys$DIIOO%&&r c[U5$)aXA DegreeView for the Graph as G.degree or G.degree(). The node degree is the number of edges adjacent to the node. The weighted node degree is the sum of the edge weights for edges incident to that node. This object provides an iterator for (node, degree) as well as lookup for the degree for a single node. Parameters ---------- nbunch : single node, container, or all nodes (default= all nodes) The view will only report edges incident to these nodes. weight : string or None, optional (default=None) The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node. Returns ------- DegreeView or int If multiple nodes are requested (the default), returns a `DegreeView` mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.degree[0] # node 0 has degree 1 1 >>> list(G.degree([0, 1, 2])) [(0, 1), (1, 2), (2, 2)] )rr6s rr Graph.degreesH$r cURR5 URR5 URR5 [R "U5 g)aRemove all nodes and edges from the graph. This also removes the name, and all graph, node, and edge attributes. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.clear() >>> list(G.nodes) [] >>> list(G.edges) [] N)rclearr-r?r4rQr6s rr Graph.clears>    r cURR5HnUR5 M [R"U5 g)zRemove all edges from the graph without altering nodes. Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.clear_edges() >>> list(G.nodes) [0, 1, 2, 3] >>> list(G.edges) [] N)rvaluesrr4rQ)rnbr_dicts r clear_edgesGraph.clear_edgess1 ((*H NN + r cg)z7Returns True if graph is a multigraph, False otherwise.Fr!r6s r is_multigraphGraph.is_multigraph%r cg)z3Returns True if graph is directed, False otherwise.Fr!r6s r is_directedGraph.is_directed)rr cxUSLa[RRU5$UR5nURR UR5 UR SURR555 URSURR555 U$)a< 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() Tc3H# UHupXR54v M g7fr)rxrrbrs rrGraph.copy..~sF3E41!VVX3Es "c3~# UH3upUR5Hup4XUR54v M M5 g7fr)rrx)rrrrrs rrrs9 ,#zz| 8==? #+ $,s;=) r4 graphviewsgeneric_graph_view __class__r?rDr}r-rrr)ras_viewGs rrx Graph.copy-sZ d?==33D9 9 NN  tzz" F4::3C3C3EFF  99??,  r cUR5nUSLa[RRX5$U"5nURR [ UR55 URSURR555 URSURR555 U$)aReturns a directed representation of the graph. Returns ------- G : DiGraph A directed graph with the same name, same nodes, and with each edge (u, v, data) replaced by two directed edges (u, v, data) and (v, u, data). Notes ----- This returns a "deepcopy" of the edge, node, and graph attributes which attempts to completely copy all of the data and references. This is in contrast to the similar D=DiGraph(G) which returns a shallow copy of the data. See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html. Warning: If you have subclassed Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method. Examples -------- >>> G = nx.Graph() # or MultiGraph, etc >>> G.add_edge(0, 1) >>> H = G.to_directed() >>> list(H.edges) [(0, 1), (1, 0)] If already directed, return a (deep) copy >>> G = nx.DiGraph() # or MultiDiGraph, etc >>> G.add_edge(0, 1) >>> H = G.to_directed() >>> list(H.edges) [(0, 1)] Tc3@# UHupU[U54v M g7frrrs rr$Graph.to_directed..I6Hda!Xa[)6Hc3t# UH.upUR5Hup4X[U54v M M0 g7frrr)rrrrrs rrrs7 ,::<8D> "' #,68) r7r4rrr?rDrr}r-rrrrr graph_classrs r to_directedGraph.to_directedsT,,. d?==33DF F M x +, Idjj6F6F6HII  99??,  r cUR5nUSLa[RRX5$U"5nURR [ UR55 URSURR555 URSURR555 U$)aReturns an undirected copy of the graph. Parameters ---------- as_view : bool (optional, default=False) If True return a view of the original undirected graph. Returns ------- G : Graph/MultiGraph A deepcopy of the graph. See Also -------- Graph, 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.DiGraph(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 DiGraph to use dict-like objects in the data structure, those changes do not transfer to the Graph 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)] Tc3@# UHupU[U54v M g7frrrs rr&Graph.to_undirected..rrc3t# UH.upUR5Hup4X[U54v M M0 g7frr)rrrrrs rrrs7 , 8A; $ ,r) r:r4rrr?rDrr}r-rrrrs r to_undirectedGraph.to_undirectedsV..0 d?==33DF F M x +, Idjj6F6F6HII  99??,  r c[RRURU55n[Rn[ US5(aU"UR X RS9$U"XS9$)aReturns a SubGraph view of the subgraph induced on `nodes`. The induced subgraph of the graph contains the nodes in `nodes` and the edges between those nodes. Parameters ---------- nodes : list, iterable A container of nodes which will be iterated through once. Returns ------- G : SubGraph View A subgraph view of the graph. The graph structure cannot be changed but node/edge attributes can and are shared with the original graph. Notes ----- The graph, edge and node attributes are shared with the original graph. Changes to the graph structure is ruled out by the view, but changes to attributes are reflected in the original graph. To create a subgraph with its own copy of the edge/node attributes use: G.subgraph(nodes).copy() For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from([n for n in G if n not in set(nodes)]) Subgraph views are sometimes NOT what you want. In most cases where you want to do more than simply look at the induced edges, it makes more sense to just create the subgraph as its own graph with code like: :: # Create a subgraph SG based on a (possibly multigraph) G SG = G.__class__() SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc) if SG.is_multigraph(): SG.add_edges_from( (n, nbr, key, d) for n, nbrs in G.adj.items() if n in largest_wcc for nbr, keydict in nbrs.items() if nbr in largest_wcc for key, d in keydict.items() ) else: SG.add_edges_from( (n, nbr, d) for n, nbrs in G.adj.items() if n in largest_wcc for nbr, d in nbrs.items() if nbr in largest_wcc ) SG.graph.update(G.graph) Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> H = G.subgraph([0, 1, 2]) >>> list(H.edges) [(0, 1), (1, 2)] _NODE_OK) filter_node filter_edge)r)r4filters show_nodes nbunch_iter subgraph_viewhasattr_graph_EDGE_OK)rr. induced_nodessubgraphs rr Graph.subgraphscB --d.>.>u.EF ## 4 $ $ MM 88r c.[R"X5$)a%Returns the subgraph induced by the specified edges. The induced subgraph contains each edge in `edges` and each node incident to any one of those edges. Parameters ---------- edges : iterable An iterable of edges in this graph. Returns ------- G : Graph An edge-induced subgraph of this graph with the same edge attributes. Notes ----- The graph, edge, and node attributes in the returned subgraph view are references to the corresponding attributes in the original graph. The view is read-only. To create a full graph version of the subgraph with its own copy of the edge or node attributes, use:: G.edge_subgraph(edges).copy() Examples -------- >>> G = nx.path_graph(5) >>> H = G.edge_subgraph([(0, 1), (3, 4)]) >>> list(H.nodes) [0, 1, 3, 4] >>> list(H.edges) [(0, 1), (3, 4)] )r4 edge_subgraph)rrs rrGraph.edge_subgraphAsL,,r cZ[SURUS955nUcUS-$US- $)a#Returns the number of edges or total of all edge weights. Parameters ---------- weight : string or None, optional (default=None) The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. Returns ------- size : numeric The number of edges or (if weight keyword is provided) the total weight sum. If weight is None, returns an int. Otherwise a float (or more general numeric if the weights are more general). See Also -------- number_of_edges Examples -------- >>> G = nx.path_graph(4) # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.size() 3 >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_edge("a", "b", weight=2) >>> G.add_edge("b", "c", weight=4) >>> G.size() 2 >>> G.size(weight="weight") 6.0 c3*# UH upUv M g7frr!)rrrs rrGraph.size..s98da8srr)sumr)rrrRs rsize Graph.sizeis9H 9dkkk89 9  qAv2QU2r cbUc[UR55$X RU;agg)aReturns the number of edges between two nodes. Parameters ---------- u, v : nodes, optional (default=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 graphs, this method counts the total number of edges in the graph: >>> G = nx.path_graph(4) >>> 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) 1 For directed graphs, this method can count the total number of directed edges from `u` to `v`: >>> G = nx.DiGraph() >>> G.add_edge(0, 1) >>> G.add_edge(1, 0) >>> G.number_of_edges(0, 1) 1 r)intrrrs rrWGraph.number_of_edgess/\ 9tyy{# # ! r cUc[UR5nU$X;a[U/5nU$SnU"XR5nU$)a@Returns an iterator over nodes contained in nbunch that are also in the graph. The nodes in nbunch are checked for membership in the graph and if not are silently ignored. Parameters ---------- nbunch : single node, container, or all nodes (default= all nodes) The view will only report edges incident to these nodes. Returns ------- niter : iterator An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph. Raises ------ NetworkXError If nbunch is not a node or sequence of nodes. If a node in nbunch is not hashable. See Also -------- Graph.__iter__ Notes ----- When nbunch is an iterator, the returned iterator yields values directly from nbunch, becoming exhausted when nbunch is exhausted. To test whether nbunch is a single node, one can use "if nbunch in self:", even after processing with this routine. If nbunch is not a node or a (possibly empty) sequence/iterator or None, a :exc:`NetworkXError` is raised. 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