MultiGraph—Undirected graphs with self loops and parallel edges¶
Overview¶
-
class
MultiGraph
(incoming_graph_data=None, **attr)[source]¶ An undirected graph class that can store multiedges.
Multiedges are multiple edges between two nodes. Each edge can hold optional data or attributes.
A MultiGraph holds undirected edges. Self loops are allowed.
Nodes can be arbitrary (hashable) Python objects with optional key/value attributes. By convention
None
is not used as a node.Edges are represented as links between nodes with optional key/value attributes.
- Parameters
incoming_graph_data (input graph (optional, default: None)) – Data to initialize graph. If None (default) an empty graph is created. The data can be any format that is supported by the to_networkx_graph() function, currently including edge list, dict of dicts, dict of lists, NetworkX graph, NumPy matrix or 2d ndarray, SciPy sparse matrix, or PyGraphviz graph.
attr (keyword arguments, optional (default= no attributes)) – Attributes to add to graph as key=value pairs.
See also
Examples
Create an empty graph structure (a “null graph”) with no nodes and no edges.
>>> G = nx.MultiGraph()
G can be grown in several ways.
Nodes:
Add one node at a time:
>>> G.add_node(1)
Add the nodes from any container (a list, dict, set or even the lines from a file or the nodes from another graph).
>>> G.add_nodes_from([2, 3]) >>> G.add_nodes_from(range(100, 110)) >>> H = nx.path_graph(10) >>> G.add_nodes_from(H)
In addition to strings and integers any hashable Python object (except None) can represent a node, e.g. a customized node object, or even another Graph.
>>> G.add_node(H)
Edges:
G can also be grown by adding edges.
Add one edge,
>>> key = G.add_edge(1, 2)
a list of edges,
>>> keys = G.add_edges_from([(1, 2), (1, 3)])
or a collection of edges,
>>> keys = G.add_edges_from(H.edges)
If some edges connect nodes not yet in the graph, the nodes are added automatically. If an edge already exists, an additional edge is created and stored using a key to identify the edge. By default the key is the lowest unused integer.
>>> keys = G.add_edges_from([(4, 5, {"route": 28}), (4, 5, {"route": 37})]) >>> G[4] AdjacencyView({3: {0: {}}, 5: {0: {}, 1: {'route': 28}, 2: {'route': 37}}})
Attributes:
Each graph, node, and edge can hold key/value attribute pairs in an associated attribute dictionary (the keys must be hashable). By default these are empty, but can be added or changed using add_edge, add_node or direct manipulation of the attribute dictionaries named graph, node and edge respectively.
>>> G = nx.MultiGraph(day="Friday") >>> G.graph {'day': 'Friday'}
Add node attributes using add_node(), add_nodes_from() or G.nodes
>>> G.add_node(1, time="5pm") >>> G.add_nodes_from([3], time="2pm") >>> G.nodes[1] {'time': '5pm'} >>> G.nodes[1]["room"] = 714 >>> del G.nodes[1]["room"] # remove attribute >>> list(G.nodes(data=True)) [(1, {'time': '5pm'}), (3, {'time': '2pm'})]
Add edge attributes using add_edge(), add_edges_from(), subscript notation, or G.edges.
>>> key = G.add_edge(1, 2, weight=4.7) >>> keys = G.add_edges_from([(3, 4), (4, 5)], color="red") >>> keys = G.add_edges_from([(1, 2, {"color": "blue"}), (2, 3, {"weight": 8})]) >>> G[1][2][0]["weight"] = 4.7 >>> G.edges[1, 2, 0]["weight"] = 4
Warning: we protect the graph data structure by making
G.edges[1, 2]
a read-only dict-like structure. However, you can assign to attributes in e.g.G.edges[1, 2]
. Thus, use 2 sets of brackets to add/change data attributes:G.edges[1, 2]['weight'] = 4
(For multigraphs:MG.edges[u, v, key][name] = value
).Shortcuts:
Many common graph features allow python syntax to speed reporting.
>>> 1 in G # check if node in graph True >>> [n for n in G if n < 3] # iterate through nodes [1, 2] >>> len(G) # number of nodes in graph 5 >>> G[1] # adjacency dict-like view keyed by neighbor to edge attributes AdjacencyView({2: {0: {'weight': 4}, 1: {'color': 'blue'}}})
Often the best way to traverse all edges of a graph is via the neighbors. The neighbors are reported as an adjacency-dict
G.adj
orG.adjacency()
.>>> for n, nbrsdict in G.adjacency(): ... for nbr, keydict in nbrsdict.items(): ... for key, eattr in keydict.items(): ... if "weight" in eattr: ... # Do something useful with the edges ... pass
But the edges() method is often more convenient:
>>> for u, v, keys, weight in G.edges(data="weight", keys=True): ... if weight is not None: ... # Do something useful with the edges ... pass
Reporting:
Simple graph information is obtained using methods and object-attributes. Reporting usually provides views instead of containers to reduce memory usage. The views update as the graph is updated similarly to dict-views. The objects
nodes, `edges
andadj
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 foredges
) Views exist fornodes
,edges
,neighbors()
/adj
anddegree
.For details on these and other miscellaneous methods, see below.
Subclasses (Advanced):
The MultiGraph class uses a dict-of-dict-of-dict-of-dict data structure. The outer dict (node_dict) holds adjacency information keyed by node. The next dict (adjlist_dict) represents the adjacency information and holds edge_key dicts keyed by neighbor. The edge_key dict holds each edge_attr dict keyed by edge key. The inner dict (edge_attr_dict) represents the edge data and holds edge attribute values keyed by attribute names.
Each of these four dicts in the dict-of-dict-of-dict-of-dict structure can be replaced by a user defined dict-like object. In general, the dict-like features should be maintained but extra features can be added. To replace one of the dicts create a new graph class by changing the class(!) variable holding the factory for that dict-like structure. The variable names are node_dict_factory, node_attr_dict_factory, adjlist_inner_dict_factory, adjlist_outer_dict_factory, edge_key_dict_factory, edge_attr_dict_factory and graph_attr_dict_factory.
- node_dict_factoryfunction, (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_factoryfunction, (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_factoryfunction, (default: dict)
Factory function to be used to create the adjacency list dict which holds multiedge key dicts keyed by neighbor. It should require no arguments and return a dict-like object.
- edge_key_dict_factoryfunction, (default: dict)
Factory function to be used to create the edge key dict which holds edge data keyed by edge key. It should require no arguments and return a dict-like object.
- edge_attr_dict_factoryfunction, (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_factoryfunction, (default: dict)
Factory function to be used to create the graph attribute dict which holds attribute values keyed by attribute name. It should require no arguments and return a dict-like object.
Typically, if your extension doesn’t impact the data structure all methods will inherited without issue except:
to_directed/to_undirected
. By default these methods create a DiGraph/Graph class and you probably want them to create your extension of a DiGraph/Graph. To facilitate this we define two class variables that you can set in your subclass.- to_directed_classcallable, (default: DiGraph or MultiDiGraph)
Class to create a new graph structure in the
to_directed
method. IfNone
, a NetworkX class (DiGraph or MultiDiGraph) is used.- to_undirected_classcallable, (default: Graph or MultiGraph)
Class to create a new graph structure in the
to_undirected
method. IfNone
, a NetworkX class (Graph or MultiGraph) is used.
Examples
Please see
ordered
for examples of creating graph subclasses by overwriting the base classdict
with a dictionary-like object.
Methods¶
Adding and removing nodes and edges¶
|
Initialize a graph with edges, name, or graph attributes. |
|
Add a single node |
|
Add multiple nodes. |
Remove node n. |
|
|
Remove multiple nodes. |
|
Add an edge between u and v. |
|
Add all the edges in ebunch_to_add. |
|
Add weighted edges in |
|
Returns an unused key for edges between nodes |
|
Remove an edge between u and v. |
|
Remove all edges specified in ebunch. |
|
Update the graph using nodes/edges/graphs as input. |
Remove all nodes and edges from the graph. |
|
Remove all edges from the graph without altering nodes. |
Reporting nodes edges and neighbors¶
A NodeView of the Graph as G.nodes or G.nodes(). |
|
Iterate over the nodes. |
|
Returns True if the graph contains the node n. |
|
Returns True if n is a node, False otherwise. |
|
Returns an iterator over the edges. |
|
|
Returns True if the graph has an edge between nodes u and v. |
|
Returns the attribute dictionary associated with edge (u, v). |
Returns an iterator over all neighbors of node n. |
|
Graph adjacency object holding the neighbors of each node. |
|
Returns a dict of neighbors of node n. |
|
Returns an iterator over (node, adjacency dict) tuples for all nodes. |
|
|
Returns an iterator over nodes contained in nbunch that are also in the graph. |
Counting nodes edges and neighbors¶
Returns the number of nodes in the graph. |
|
Returns the number of nodes in the graph. |
|
Returns the number of nodes in the graph. |
|
A DegreeView for the Graph as G.degree or G.degree(). |
|
|
Returns the number of edges or total of all edge weights. |
|
Returns the number of edges between two nodes. |
Making copies and subgraphs¶
|
Returns a copy of the graph. |
|
Returns an undirected copy of the graph. |
|
Returns a directed representation of the graph. |
|
Returns a SubGraph view of the subgraph induced on |
|
Returns the subgraph induced by the specified edges. |