causalnex.structure.StructureModel

class causalnex.structure.StructureModel(incoming_graph_data=None, origin='unknown', **attr)[source]

Bases: networkx.classes.digraph.DiGraph

Base class for structure models, which are an extension of networkx.DiGraph.

A StructureModel stores nodes and edges with optional data, or attributes.

Edges have one required attribute, “origin”, which describes how the edge was created. Origin can be one of either unknown, learned, or expert.

StructureModel hold directed edges, describing a cause -> effect relationship. Cycles are permitted within a StructureModel.

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.

Attributes

StructureModel.adj Graph adjacency object holding the neighbors of each node.
StructureModel.degree A DegreeView for the Graph as G.degree or G.degree().
StructureModel.edges An OutEdgeView of the DiGraph as G.edges or G.edges().
StructureModel.in_degree An InDegreeView for (node, in_degree) or in_degree for single node.
StructureModel.in_edges An InEdgeView of the Graph as G.in_edges or G.in_edges().
StructureModel.name String identifier of the graph.
StructureModel.nodes A NodeView of the Graph as G.nodes or G.nodes().
StructureModel.out_degree An OutDegreeView for (node, out_degree)
StructureModel.out_edges An OutEdgeView of the DiGraph as G.edges or G.edges().
StructureModel.pred Graph adjacency object holding the predecessors of each node.
StructureModel.succ Graph adjacency object holding the successors of each node.

Methods

StructureModel.__init__([…]) Create a StructureModel with incoming_graph_data, which has come from some origin.
StructureModel.add_edge(u_of_edge, v_of_edge) Adds a causal relationship from u to v.
StructureModel.add_edges_from(ebunch_to_add) Adds a bunch of causal relationships, u -> v.
StructureModel.add_node(node_for_adding, **attr) Add a single node node_for_adding and update node attributes.
StructureModel.add_nodes_from(…) Add multiple nodes.
StructureModel.add_weighted_edges_from(…) Adds a bunch of weighted causal relationships, u -> v.
StructureModel.adjacency() Returns an iterator over (node, adjacency dict) tuples for all nodes.
StructureModel.clear() Remove all nodes and edges from the graph.
StructureModel.copy([as_view]) Returns a copy of the graph.
StructureModel.edge_subgraph(edges) Returns the subgraph induced by the specified edges.
StructureModel.edges_with_origin(origin) List of edges created with given origin attribute.
StructureModel.get_edge_data(u, v[, default]) Returns the attribute dictionary associated with edge (u, v).
StructureModel.get_largest_subgraph() Get the largest subgraph of the Structure Model.
StructureModel.get_target_subgraph(node) Get the subgraph with the specified node.
StructureModel.has_edge(u, v) Returns True if the edge (u, v) is in the graph.
StructureModel.has_node(n) Returns True if the graph contains the node n.
StructureModel.has_predecessor(u, v) Returns True if node u has predecessor v.
StructureModel.has_successor(u, v) Returns True if node u has successor v.
StructureModel.is_directed() Returns True if graph is directed, False otherwise.
StructureModel.is_multigraph() Returns True if graph is a multigraph, False otherwise.
StructureModel.nbunch_iter([nbunch]) Returns an iterator over nodes contained in nbunch that are also in the graph.
StructureModel.neighbors(n) Returns an iterator over successor nodes of n.
StructureModel.number_of_edges([u, v]) Returns the number of edges between two nodes.
StructureModel.number_of_nodes() Returns the number of nodes in the graph.
StructureModel.order() Returns the number of nodes in the graph.
StructureModel.predecessors(n) Returns an iterator over predecessor nodes of n.
StructureModel.remove_edge(u, v) Remove the edge between u and v.
StructureModel.remove_edges_below_threshold(…) Remove edges whose absolute weights are less than a defined threshold.
StructureModel.remove_edges_from(ebunch) Remove all edges specified in ebunch.
StructureModel.remove_node(n) Remove node n.
StructureModel.remove_nodes_from(nodes) Remove multiple nodes.
StructureModel.reverse([copy]) Returns the reverse of the graph.
StructureModel.size([weight]) Returns the number of edges or total of all edge weights.
StructureModel.subgraph(nodes) Returns a SubGraph view of the subgraph induced on nodes.
StructureModel.successors(n) Returns an iterator over successor nodes of n.
StructureModel.threshold_till_dag() Remove edges with smallest weight until the graph is a DAG.
StructureModel.to_directed([as_view]) Returns a directed representation of the graph.
StructureModel.to_directed_class() Returns the class to use for directed copies.
StructureModel.to_undirected([reciprocal, …]) Returns an undirected representation of the digraph.
StructureModel.to_undirected_class() Returns the class to use for undirected copies.
StructureModel.update([edges, nodes]) Update the graph using nodes/edges/graphs as input.
__init__(incoming_graph_data=None, origin='unknown', **attr)[source]

Create a StructureModel with incoming_graph_data, which has come from some origin.

Parameters:
  • incoming_graph_data (Optional) – 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.
  • origin (str) – label for how the edges were created. Can be one of: - unknown: edges exist for an unknown reason; - learned: edges were created as the output of a machine-learning process; - expert: edges were created by a domain expert.
  • attr – Attributes to add to graph as key/value pairs (no attributes by default).
add_edge(u_of_edge, v_of_edge, origin='unknown', **attr)[source]

Adds a causal relationship from u to v.

If u or v do not currently exists in the StructureModel then they will be created.

By default a relationship will be given origin=”unknown”, but may also be given “learned” or “expert” origin.

Adding an edge that already exists will replace the existing edge. See networkx.DiGraph.add_edge().

Parameters:
  • u_of_edge (str) – causal node.
  • v_of_edge (str) – effect node.
  • origin (str) – label for how the edge was created. Can be one of: - unknown: edge exists for an unknown reason; - learned: edge was created as the output of a machine-learning process; - expert: edge was created by a domain expert.
  • **attr – Attributes to add to edge as key/value pairs (no attributes by default).
add_edges_from(ebunch_to_add, origin='unknown', **attr)[source]

Adds a bunch of causal relationships, u -> v.

If u or v do not currently exists in the StructureModel then they will be created.

By default relationships will be given origin=”unknown”, but may also be given “learned” or “expert” origin.

Notes

Adding an edge that already exists will replace the existing edge. See networkx.DiGraph.add_edges_from().

Parameters:
  • ebunch_to_add (Union[Set[tuple], List[tuple]]) – container of edges. Each edge given in the container will be added to the graph. The edges must be given as 2-tuples (u, v) or 3-tuples (u, v, d) where d is a dictionary containing edge data.
  • origin (str) – label for how the edges were created. One of: - unknown: edges exist for an unknown reason. - learned: edges were created as the output of a machine-learning process. - expert: edges were created by a domain expert.
  • **attr – Attributes to add to edge as key/value pairs (no attributes by default).
add_node(node_for_adding, **attr)

Add 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()

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.

add_nodes_from(nodes_for_adding, **attr)

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()

[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

add_weighted_edges_from(ebunch_to_add, weight='weight', origin='unknown', **attr)[source]

Adds a bunch of weighted causal relationships, u -> v.

If u or v do not currently exists in the StructureModel then they will be created.

By default relationships will be given origin=”unknown”, but may also be given “learned” or “expert” origin.

Notes

Adding an edge that already exists will replace the existing edge. See networkx.DiGraph.add_edges_from().

Parameters:
  • ebunch_to_add (Union[Set[tuple], List[tuple]]) – container of edges. Each edge given in the container will be added to the graph. The edges must be given as 2-tuples (u, v) or 3-tuples (u, v, d) where d is a dictionary containing edge data.
  • weight (str) – string, optional (default=’weight’). The attribute name for the edge weights to be added.
  • origin (str) – label for how the edges were created. One of: - unknown: edges exist for an unknown reason; - learned: edges were created as the output of a machine-learning process; - expert: edges were created by a domain expert.
  • **attr – Attributes to add to edge as key/value pairs (no attributes by default).
adj

Graph adjacency object holding the neighbors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the 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.

adjacency()

Returns an iterator over (node, adjacency dict) tuples for all nodes.

For directed graphs, only outgoing neighbors/adjacencies are included.

Returns:adj_iter – An iterator over (node, adjacency dictionary) for all nodes in the graph.
Return type:iterator

[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]

adjlist_inner_dict_factory

alias of builtins.dict

adjlist_outer_dict_factory

alias of builtins.dict

clear()

Remove all nodes and edges from the graph.

This also removes the name, and all graph, node, and edge attributes.

[]
list(G.edges)

[]

copy(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 – A copy of the graph.
Return type:Graph

See also

to_directed()
return a directed copy of the graph.
degree

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
  • OR if multiple nodes are requested
  • nd_iter (iterator) – The iterator returns two-tuples of (node, degree).

See also

in_degree, out_degree

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

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

edge_attr_dict_factory

alias of builtins.dict

edge_subgraph(edges)

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 – An edge-induced subgraph of this graph with the same edge attributes.
Return type:Graph

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()  # doctest: +SKIP
[0, 1, 3, 4]
list(H.edges)

[(0, 1), (3, 4)]

edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

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

The OutEdgeView 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 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).
  • 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 – 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’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

[(0, 1), (1, 2), (2, 3)]
G.edges.data() # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {‘weight’: 5})])
G.edges.data(‘weight’, default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
G.edges([0, 2]) # only edges incident to these nodes
OutEdgeDataView([(0, 1), (2, 3)])
G.edges(0) # only edges incident to a single node (use G.adj[0]?)

OutEdgeDataView([(0, 1)])

edges_with_origin(origin)[source]

List of edges created with given origin attribute.

Return type:list
Returns:A list of edges with the given origin.
get_edge_data(u, v, default=None)

Returns 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:
  • v (u,) –
  • default (any Python object (default=None)) – Value to return if the edge (u, v) is not found.
Returns:

edge_dict – The edge attribute dictionary.

Return type:

dictionary

{}

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

get_largest_subgraph()[source]

Get the largest subgraph of the Structure Model.

Return type:StructureModel
Returns:The largest subgraph of the Structure Model. If no subgraph exists, None is returned.
get_target_subgraph(node)[source]

Get the subgraph with the specified node.

Parameters:node (Hashable) – the name of the node.
Return type:StructureModel
Returns:The subgraph with the target node.
Raises:NodeNotFound – if the node is not found in the graph.
graph_attr_dict_factory

alias of builtins.dict

has_edge(u, v)

Returns True if the edge (u, v) is in the graph.

This is the same as v in G[u] without KeyError exceptions.

Parameters:v (u,) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.
Returns:edge_ind – True if edge is in the graph, False otherwise.
Return type:bool
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

has_node(n)

Returns True if the graph contains the node n.

Identical to n in G

Parameters:n (node) –

True

It is more readable and simpler to use

0 in G

True

has_predecessor(u, v)

Returns True if node u has predecessor v.

This is true if graph has the edge u<-v.

has_successor(u, v)

Returns True if node u has successor v.

This is true if graph has the edge u->v.

in_degree

An InDegreeView for (node, in_degree) or in_degree for single node.

The node in_degree is the number of edges pointing to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iteration over (node, in_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) – In-degree of the node
  • OR if multiple nodes are requested
  • nd_iter (iterator) – The iterator returns two-tuples of (node, in-degree).

See also

degree, out_degree

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

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

in_edges

An InEdgeView of the Graph as G.in_edges or G.in_edges().

in_edges(self, nbunch=None, data=False, default=None):

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).
  • 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:

in_edges – 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’].

Return type:

InEdgeView

See also

edges

is_directed()

Returns True if graph is directed, False otherwise.

is_multigraph()

Returns True if graph is a multigraph, False otherwise.

name

String 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.

nbunch_iter(nbunch=None)

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 – An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph.
Return type:iterator
Raises:NetworkXError – If nbunch is not a node or 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 NetworkXError is raised. Also, if any object in nbunch is not hashable, a NetworkXError is raised.

neighbors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:n (node) – A node in the graph
Raises:NetworkXError – If n is not in the graph.

See also

predecessors()

Notes

neighbors() and successors() are the same.

node_attr_dict_factory

alias of builtins.dict

node_dict_factory

alias of builtins.dict

nodes

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:

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.

Return type:

NodeView

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}
number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters:v (u,) – 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 – 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.
Return type:int

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

number_of_nodes()

Returns the number of nodes in the graph.

Returns:nnodes – The number of nodes in the graph.
Return type:int

See also

order(), __len__()

3

order()

Returns the number of nodes in the graph.

Returns:nnodes – The number of nodes in the graph.
Return type:int

See also

number_of_nodes(), __len__()

3

out_degree

An OutDegreeView for (node, out_degree)

The node out_degree is the number of edges pointing out of the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator over (node, out_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) – Out-degree of the node
  • OR if multiple nodes are requested
  • nd_iter (iterator) – The iterator returns two-tuples of (node, out-degree).

See also

degree, in_degree

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

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

out_edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

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

The OutEdgeView 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 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).
  • 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 – 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’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

[(0, 1), (1, 2), (2, 3)]
G.edges.data() # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {‘weight’: 5})])
G.edges.data(‘weight’, default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
G.edges([0, 2]) # only edges incident to these nodes
OutEdgeDataView([(0, 1), (2, 3)])
G.edges(0) # only edges incident to a single node (use G.adj[0]?)

OutEdgeDataView([(0, 1)])

pred

Graph adjacency object holding the predecessors 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.pred[2][3][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.pred behaves like a dict. Useful idioms include for nbr, datadict in G.pred[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.pred[node].data(‘foo’): A default can be set via a default argument to the data method.

predecessors(n)

Returns an iterator over predecessor nodes of n.

A predecessor of n is a node m such that there exists a directed edge from m to n.

Parameters:n (node) – A node in the graph
Raises:NetworkXError – If n is not in the graph.

See also

successors()

remove_edge(u, v)

Remove the edge between u and v.

Parameters:v (u,) – 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
remove_edges_below_threshold(threshold)[source]

Remove edges whose absolute weights are less than a defined threshold.

Parameters:threshold (float) – edges whose absolute weight is less than this value are removed.
remove_edges_from(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) 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.

remove_node(n)

Remove node n.

Removes the node n and all adjacent edges. Attempting to remove a non-existent node will raise an exception.

Parameters:n (node) – A node in the graph
Raises:NetworkXError – If n is not in the graph.
[(0, 1), (1, 2)]
G.remove_node(1) list(G.edges)

[]

remove_nodes_from(nodes)

Remove multiple nodes.

Parameters:nodes (iterable container) – A container of nodes (list, dict, set, etc.). If a node in the container is not in the graph it is silently ignored.

See also

remove_node()

[0, 1, 2]
G.remove_nodes_from(e) list(G.nodes)

[]

reverse(copy=True)

Returns the reverse of the graph.

The reverse is a graph with the same nodes and edges but with the directions of the edges reversed.

Parameters:copy (bool optional (default=True)) – If True, return a new DiGraph holding the reversed edges. If False, the reverse graph is created using a view of the original graph.
size(weight=None)

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 – 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).

Return type:numeric

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

subgraph(nodes)

Returns 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 – A subgraph view of the graph. The graph structure cannot be changed but node/edge attributes can and are shared with the original graph.
Return type:SubGraph View

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)

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

succ

Graph adjacency object holding the successors 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.succ[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.succ behaves like a dict. Useful idioms include for nbr, datadict in G.succ[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.succ[node].data(‘foo’): and a default can be set via a default argument to the data method.

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 is identical to G.succ.

successors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:n (node) – A node in the graph
Raises:NetworkXError – If n is not in the graph.

See also

predecessors()

Notes

neighbors() and successors() are the same.

threshold_till_dag()[source]

Remove edges with smallest weight until the graph is a DAG. Not recommended if the weights have different units.

to_directed(as_view=False)

Returns a directed representation of the graph.

Returns:G – 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).
Return type:DiGraph

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 Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method.

[(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)]

to_directed_class()[source]

Returns the class to use for directed copies. See networkx.DiGraph.to_directed().

to_undirected(reciprocal=False, as_view=False)

Returns an undirected representation of the digraph.

Parameters:
  • reciprocal (bool (optional)) – If True only keep edges that appear in both directions in the original digraph.
  • as_view (bool (optional, default=False)) – If True return an undirected view of the original directed graph.
Returns:

G – An undirected graph with the same name and nodes and with edge (u, v, data) if either (u, v, data) or (v, u, data) is in the digraph. If both edges exist in digraph and their edge data is different, only one edge is created with an arbitrary choice of which edge data to use. You must check and correct for this manually if desired.

Return type:

Graph

See also

Graph(), copy(), add_edge(), add_edges_from()

Notes

If edges in both directions (u, v) and (v, u) exist in the graph, attributes for the new undirected edge will be a combination of the attributes of the directed edges. The edge data is updated in the (arbitrary) order that the edges are encountered. For more customized control of the edge attributes use add_edge().

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=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/2/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.

[(0, 1), (1, 0)]
G2 = H.to_undirected() list(G2.edges)

[(0, 1)]

to_undirected_class()[source]

Returns the class to use for undirected copies. See networkx.DiGraph.to_undirected().

update(edges=None, nodes=None)

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.

… 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