1140 lines
40 KiB
Python
1140 lines
40 KiB
Python
# Copyright (C) 2004-2019 by
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# Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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# All rights reserved.
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# BSD license.
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#
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# Authors: Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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"""Base class for MultiGraph."""
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from copy import deepcopy
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import networkx as nx
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from networkx.classes.graph import Graph
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from networkx.classes.coreviews import MultiAdjacencyView
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from networkx.classes.reportviews import MultiEdgeView, MultiDegreeView
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from networkx import NetworkXError
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from networkx.utils import iterable
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class MultiGraph(Graph):
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"""
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An undirected graph class that can store multiedges.
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Multiedges are multiple edges between two nodes. Each edge
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can hold optional data or attributes.
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A MultiGraph holds undirected edges. Self loops are allowed.
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Nodes can be arbitrary (hashable) Python objects with optional
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key/value attributes. By convention `None` is not used as a node.
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Edges are represented as links between nodes with optional
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key/value attributes.
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Parameters
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----------
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incoming_graph_data : input graph (optional, default: None)
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Data to initialize graph. If None (default) an empty
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graph is created. The data can be any format that is supported
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by the to_networkx_graph() function, currently including edge list,
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dict of dicts, dict of lists, NetworkX graph, NumPy matrix
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or 2d ndarray, SciPy sparse matrix, or PyGraphviz graph.
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attr : keyword arguments, optional (default= no attributes)
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Attributes to add to graph as key=value pairs.
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See Also
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--------
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Graph
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DiGraph
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MultiDiGraph
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OrderedMultiGraph
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Examples
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--------
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Create an empty graph structure (a "null graph") with no nodes and
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no edges.
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>>> G = nx.MultiGraph()
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G can be grown in several ways.
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**Nodes:**
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Add one node at a time:
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>>> G.add_node(1)
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Add the nodes from any container (a list, dict, set or
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even the lines from a file or the nodes from another graph).
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>>> G.add_nodes_from([2, 3])
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>>> G.add_nodes_from(range(100, 110))
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>>> H = nx.path_graph(10)
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>>> G.add_nodes_from(H)
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In addition to strings and integers any hashable Python object
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(except None) can represent a node, e.g. a customized node object,
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or even another Graph.
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>>> G.add_node(H)
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**Edges:**
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G can also be grown by adding edges.
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Add one edge,
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>>> key = G.add_edge(1, 2)
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a list of edges,
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>>> keys = G.add_edges_from([(1, 2), (1, 3)])
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or a collection of edges,
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>>> keys = G.add_edges_from(H.edges)
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If some edges connect nodes not yet in the graph, the nodes
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are added automatically. If an edge already exists, an additional
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edge is created and stored using a key to identify the edge.
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By default the key is the lowest unused integer.
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>>> keys = G.add_edges_from([(4,5,{'route':28}), (4,5,{'route':37})])
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>>> G[4]
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AdjacencyView({3: {0: {}}, 5: {0: {}, 1: {'route': 28}, 2: {'route': 37}}})
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**Attributes:**
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Each graph, node, and edge can hold key/value attribute pairs
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in an associated attribute dictionary (the keys must be hashable).
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By default these are empty, but can be added or changed using
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add_edge, add_node or direct manipulation of the attribute
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dictionaries named graph, node and edge respectively.
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>>> G = nx.MultiGraph(day="Friday")
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>>> G.graph
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{'day': 'Friday'}
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Add node attributes using add_node(), add_nodes_from() or G.nodes
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>>> G.add_node(1, time='5pm')
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>>> G.add_nodes_from([3], time='2pm')
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>>> G.nodes[1]
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{'time': '5pm'}
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>>> G.nodes[1]['room'] = 714
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>>> del G.nodes[1]['room'] # remove attribute
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>>> list(G.nodes(data=True))
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[(1, {'time': '5pm'}), (3, {'time': '2pm'})]
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Add edge attributes using add_edge(), add_edges_from(), subscript
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notation, or G.edges.
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>>> key = G.add_edge(1, 2, weight=4.7 )
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>>> keys = G.add_edges_from([(3, 4), (4, 5)], color='red')
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>>> keys = G.add_edges_from([(1,2,{'color':'blue'}), (2,3,{'weight':8})])
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>>> G[1][2][0]['weight'] = 4.7
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>>> G.edges[1, 2, 0]['weight'] = 4
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Warning: we protect the graph data structure by making `G.edges[1, 2]` a
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read-only dict-like structure. However, you can assign to attributes
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in e.g. `G.edges[1, 2]`. Thus, use 2 sets of brackets to add/change
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data attributes: `G.edges[1, 2]['weight'] = 4`
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(For multigraphs: `MG.edges[u, v, key][name] = value`).
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**Shortcuts:**
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Many common graph features allow python syntax to speed reporting.
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>>> 1 in G # check if node in graph
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True
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>>> [n for n in G if n<3] # iterate through nodes
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[1, 2]
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>>> len(G) # number of nodes in graph
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5
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>>> G[1] # adjacency dict-like view keyed by neighbor to edge attributes
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AdjacencyView({2: {0: {'weight': 4}, 1: {'color': 'blue'}}})
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Often the best way to traverse all edges of a graph is via the neighbors.
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The neighbors are reported as an adjacency-dict `G.adj` or `G.adjacency()`.
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>>> for n, nbrsdict in G.adjacency():
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... for nbr, keydict in nbrsdict.items():
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... for key, eattr in keydict.items():
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... if 'weight' in eattr:
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... # Do something useful with the edges
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... pass
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But the edges() method is often more convenient:
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>>> for u, v, keys, weight in G.edges(data='weight', keys=True):
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... if weight is not None:
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... # Do something useful with the edges
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... pass
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**Reporting:**
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Simple graph information is obtained using methods and object-attributes.
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Reporting usually provides views instead of containers to reduce memory
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usage. The views update as the graph is updated similarly to dict-views.
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The objects `nodes, `edges` and `adj` provide access to data attributes
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via lookup (e.g. `nodes[n], `edges[u, v]`, `adj[u][v]`) and iteration
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(e.g. `nodes.items()`, `nodes.data('color')`,
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`nodes.data('color', default='blue')` and similarly for `edges`)
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Views exist for `nodes`, `edges`, `neighbors()`/`adj` and `degree`.
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For details on these and other miscellaneous methods, see below.
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**Subclasses (Advanced):**
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The MultiGraph class uses a dict-of-dict-of-dict-of-dict data structure.
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The outer dict (node_dict) holds adjacency information keyed by node.
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The next dict (adjlist_dict) represents the adjacency information and holds
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edge_key dicts keyed by neighbor. The edge_key dict holds each edge_attr
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dict keyed by edge key. The inner dict (edge_attr_dict) represents
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the edge data and holds edge attribute values keyed by attribute names.
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Each of these four dicts in the dict-of-dict-of-dict-of-dict
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structure can be replaced by a user defined dict-like object.
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In general, the dict-like features should be maintained but
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extra features can be added. To replace one of the dicts create
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a new graph class by changing the class(!) variable holding the
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factory for that dict-like structure. The variable names are
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node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory,
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adjlist_outer_dict_factory, edge_key_dict_factory, edge_attr_dict_factory
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and graph_attr_dict_factory.
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node_dict_factory : function, (default: dict)
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Factory function to be used to create the dict containing node
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attributes, keyed by node id.
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It should require no arguments and return a dict-like object
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node_attr_dict_factory: function, (default: dict)
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Factory function to be used to create the node attribute
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dict which holds attribute values keyed by attribute name.
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It should require no arguments and return a dict-like object
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adjlist_outer_dict_factory : function, (default: dict)
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Factory function to be used to create the outer-most dict
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in the data structure that holds adjacency info keyed by node.
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It should require no arguments and return a dict-like object.
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adjlist_inner_dict_factory : function, (default: dict)
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Factory function to be used to create the adjacency list
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dict which holds multiedge key dicts keyed by neighbor.
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It should require no arguments and return a dict-like object.
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edge_key_dict_factory : function, (default: dict)
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Factory function to be used to create the edge key dict
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which holds edge data keyed by edge key.
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It should require no arguments and return a dict-like object.
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edge_attr_dict_factory : function, (default: dict)
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Factory function to be used to create the edge attribute
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dict which holds attribute values keyed by attribute name.
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It should require no arguments and return a dict-like object.
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graph_attr_dict_factory : function, (default: dict)
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Factory function to be used to create the graph attribute
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dict which holds attribute values keyed by attribute name.
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It should require no arguments and return a dict-like object.
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Typically, if your extension doesn't impact the data structure all
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methods will inherited without issue except: `to_directed/to_undirected`.
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By default these methods create a DiGraph/Graph class and you probably
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want them to create your extension of a DiGraph/Graph. To facilitate
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this we define two class variables that you can set in your subclass.
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to_directed_class : callable, (default: DiGraph or MultiDiGraph)
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Class to create a new graph structure in the `to_directed` method.
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If `None`, a NetworkX class (DiGraph or MultiDiGraph) is used.
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to_undirected_class : callable, (default: Graph or MultiGraph)
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Class to create a new graph structure in the `to_undirected` method.
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If `None`, a NetworkX class (Graph or MultiGraph) is used.
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Examples
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--------
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Please see :mod:`~networkx.classes.ordered` for examples of
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creating graph subclasses by overwriting the base class `dict` with
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a dictionary-like object.
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"""
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# node_dict_factory = dict # already assigned in Graph
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# adjlist_outer_dict_factory = dict
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# adjlist_inner_dict_factory = dict
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edge_key_dict_factory = dict
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# edge_attr_dict_factory = dict
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def to_directed_class(self):
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"""Returns the class to use for empty directed copies.
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If you subclass the base classes, use this to designate
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what directed class to use for `to_directed()` copies.
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"""
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return nx.MultiDiGraph
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def to_undirected_class(self):
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"""Returns the class to use for empty undirected copies.
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If you subclass the base classes, use this to designate
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what directed class to use for `to_directed()` copies.
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"""
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return MultiGraph
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def __init__(self, incoming_graph_data=None, **attr):
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"""Initialize a graph with edges, name, or graph attributes.
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Parameters
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----------
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incoming_graph_data : input graph
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Data to initialize graph. If incoming_graph_data=None (default)
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an empty graph is created. The data can be an edge list, or any
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NetworkX graph object. If the corresponding optional Python
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packages are installed the data can also be a NumPy matrix
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or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph.
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attr : keyword arguments, optional (default= no attributes)
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Attributes to add to graph as key=value pairs.
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See Also
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--------
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convert
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Examples
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--------
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>>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc
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>>> G = nx.Graph(name='my graph')
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>>> e = [(1, 2), (2, 3), (3, 4)] # list of edges
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>>> G = nx.Graph(e)
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Arbitrary graph attribute pairs (key=value) may be assigned
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>>> G = nx.Graph(e, day="Friday")
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>>> G.graph
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{'day': 'Friday'}
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"""
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self.edge_key_dict_factory = self.edge_key_dict_factory
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Graph.__init__(self, incoming_graph_data, **attr)
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@property
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def adj(self):
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"""Graph adjacency object holding the neighbors of each node.
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This object is a read-only dict-like structure with node keys
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and neighbor-dict values. The neighbor-dict is keyed by neighbor
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to the edgekey-data-dict. So `G.adj[3][2][0]['color'] = 'blue'` sets
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the color of the edge `(3, 2, 0)` to `"blue"`.
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Iterating over G.adj behaves like a dict. Useful idioms include
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`for nbr, nbrdict in G.adj[n].items():`.
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The neighbor information is also provided by subscripting the graph.
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So `for nbr, foovalue in G[node].data('foo', default=1):` works.
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For directed graphs, `G.adj` holds outgoing (successor) info.
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"""
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return MultiAdjacencyView(self._adj)
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def new_edge_key(self, u, v):
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"""Returns an unused key for edges between nodes `u` and `v`.
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The nodes `u` and `v` do not need to be already in the graph.
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Notes
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-----
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In the standard MultiGraph class the new key is the number of existing
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edges between `u` and `v` (increased if necessary to ensure unused).
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The first edge will have key 0, then 1, etc. If an edge is removed
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further new_edge_keys may not be in this order.
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Parameters
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----------
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u, v : nodes
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Returns
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-------
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key : int
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"""
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try:
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keydict = self._adj[u][v]
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except KeyError:
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return 0
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key = len(keydict)
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while key in keydict:
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key += 1
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return key
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def add_edge(self, u_for_edge, v_for_edge, key=None, **attr):
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"""Add an edge between u and v.
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The nodes u and v will be automatically added if they are
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not already in the graph.
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Edge attributes can be specified with keywords or by directly
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accessing the edge's attribute dictionary. See examples below.
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Parameters
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----------
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u_for_edge, v_for_edge : nodes
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Nodes can be, for example, strings or numbers.
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Nodes must be hashable (and not None) Python objects.
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key : hashable identifier, optional (default=lowest unused integer)
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Used to distinguish multiedges between a pair of nodes.
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attr : keyword arguments, optional
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Edge data (or labels or objects) can be assigned using
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keyword arguments.
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Returns
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-------
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The edge key assigned to the edge.
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See Also
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--------
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add_edges_from : add a collection of edges
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Notes
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-----
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To replace/update edge data, use the optional key argument
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to identify a unique edge. Otherwise a new edge will be created.
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NetworkX algorithms designed for weighted graphs cannot use
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multigraphs directly because it is not clear how to handle
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multiedge weights. Convert to Graph using edge attribute
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'weight' to enable weighted graph algorithms.
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Default keys are generated using the method `new_edge_key()`.
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This method can be overridden by subclassing the base class and
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providing a custom `new_edge_key()` method.
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Examples
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--------
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The following all add the edge e=(1, 2) to graph G:
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>>> G = nx.MultiGraph()
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>>> e = (1, 2)
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>>> ekey = G.add_edge(1, 2) # explicit two-node form
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>>> G.add_edge(*e) # single edge as tuple of two nodes
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1
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>>> G.add_edges_from( [(1, 2)] ) # add edges from iterable container
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[2]
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Associate data to edges using keywords:
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>>> ekey = G.add_edge(1, 2, weight=3)
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>>> ekey = G.add_edge(1, 2, key=0, weight=4) # update data for key=0
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>>> ekey = G.add_edge(1, 3, weight=7, capacity=15, length=342.7)
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For non-string attribute keys, use subscript notation.
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>>> ekey = G.add_edge(1, 2)
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>>> G[1][2][0].update({0: 5})
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>>> G.edges[1, 2, 0].update({0: 5})
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"""
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u, v = u_for_edge, v_for_edge
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# add nodes
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if u not in self._adj:
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self._adj[u] = self.adjlist_inner_dict_factory()
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self._node[u] = self.node_attr_dict_factory()
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if v not in self._adj:
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self._adj[v] = self.adjlist_inner_dict_factory()
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self._node[v] = self.node_attr_dict_factory()
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if key is None:
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key = self.new_edge_key(u, v)
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if v in self._adj[u]:
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keydict = self._adj[u][v]
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datadict = keydict.get(key, self.edge_attr_dict_factory())
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datadict.update(attr)
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keydict[key] = datadict
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else:
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# selfloops work this way without special treatment
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datadict = self.edge_attr_dict_factory()
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datadict.update(attr)
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keydict = self.edge_key_dict_factory()
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keydict[key] = datadict
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self._adj[u][v] = keydict
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self._adj[v][u] = keydict
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return key
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def add_edges_from(self, ebunch_to_add, **attr):
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"""Add all the edges in ebunch_to_add.
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Parameters
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----------
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ebunch_to_add : container of edges
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Each edge given in the container will be added to the
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graph. The edges can be:
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- 2-tuples (u, v) or
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- 3-tuples (u, v, d) for an edge data dict d, or
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- 3-tuples (u, v, k) for not iterable key k, or
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- 4-tuples (u, v, k, d) for an edge with data and key k
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attr : keyword arguments, optional
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Edge data (or labels or objects) can be assigned using
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keyword arguments.
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Returns
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-------
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A list of edge keys assigned to the edges in `ebunch`.
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See Also
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--------
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add_edge : add a single edge
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add_weighted_edges_from : convenient way to add weighted edges
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Notes
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-----
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Adding the same edge twice has no effect but any edge data
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will be updated when each duplicate edge is added.
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Edge attributes specified in an ebunch take precedence over
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attributes specified via keyword arguments.
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Default keys are generated using the method ``new_edge_key()``.
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This method can be overridden by subclassing the base class and
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providing a custom ``new_edge_key()`` method.
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Examples
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--------
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>>> 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 = "Edge tuple {} must be a 2-tuple, 3-tuple or 4-tuple."
|
|
raise NetworkXError(msg.format(e))
|
|
ddd = {}
|
|
ddd.update(attr)
|
|
try:
|
|
ddd.update(dd)
|
|
except:
|
|
if ne != 3:
|
|
raise
|
|
key = dd
|
|
key = self.add_edge(u, v, key)
|
|
self[u][v][key].update(ddd)
|
|
keylist.append(key)
|
|
return keylist
|
|
|
|
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:
|
|
raise NetworkXError(
|
|
"The edge %s-%s is not in the graph." % (u, v))
|
|
# remove the edge with specified data
|
|
if key is None:
|
|
d.popitem()
|
|
else:
|
|
try:
|
|
del d[key]
|
|
except KeyError:
|
|
msg = "The edge %s-%s with key %s is not in the graph."
|
|
raise NetworkXError(msg % (u, v, key))
|
|
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]
|
|
|
|
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
|
|
|
|
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)
|
|
|
|
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
|
|
|
|
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/2/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
|
|
|
|
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/2/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
|
|
|
|
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/2/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
|
|
|
|
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)
|