# flamingpy.codes.EGraph¶

class flamingpy.codes.EGraph(*args, indexer='default', macronodes=False, **kwargs)[source]

Bases: networkx.classes.graph.Graph

An enhanced graph for representing quantum graph states.

A class that builds on a NetworkX graph to better represent graph states. Includes indexing, drawing, and convenience methods.

macro_to_micro

if macronodes is set to True, the macro_dict object from the underlying graph (None or a dictionary of the form {central coordinate of macronode: [all micronode coordinates]})

Type

dict

to_indices

if self.index_generator() has been run, a dictionary of the form {points: indices}

Type

dict

to_points

if self.index_generator() has been run, a dictionary of the form {indices: points}

Type

dict

Type

np.array

 adj Graph adjacency object holding the neighbors of each node. degree A DegreeView for the Graph as G.degree or G.degree(). edges An EdgeView of the Graph as G.edges or G.edges(). name String identifier of the graph. nodes A NodeView of the Graph as G.nodes or G.nodes().

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”.

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.

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 multiple nodes are requested (the default), returns a DegreeView mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer.

Return type

DegreeView or int

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.degree[0]  # node 0 has degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]

edges

An EdgeView of the Graph as G.edges or G.edges().

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

The EdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters
• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.

• data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

• default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns

edges – 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

EdgeView

Notes

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

Examples

>>> G = nx.path_graph(3)  # or MultiGraph, etc
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
EdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
EdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 3])  # only edges from these nodes
EdgeDataView([(0, 1), (3, 2)])
>>> G.edges(0)  # only edges from node 0
EdgeDataView([(0, 1)])

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.

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()
>>> dict(G.nodes(data="weight", default=1))
{0: 1, 1: 2, 2: 3}

 add_edge(u_of_edge, v_of_edge, **attr) Add an edge between u and v. add_edges_from(ebunch_to_add, **attr) Add all the edges in ebunch_to_add. add_node(node_for_adding, **attr) Add a single node node_for_adding and update node attributes. add_nodes_from(nodes_for_adding, **attr) Add multiple nodes. add_qubit([qubit, neighbors, add_to_macronode]) Add qubit to EGraph connected to neighbors. add_weighted_edges_from(ebunch_to_add[, weight]) Add weighted edges in ebunch_to_add with specified weight attr adj_generator([sparse]) Return the correctly indexed adjacency matrix of the graph and set the self.adj_mat attribute. Returns an iterator over (node, adjacency dict) tuples for all nodes. Remove all nodes and edges from the graph. Remove all edges from the graph without altering nodes. copy([as_view]) Returns a copy of the graph. draw([backend]) Draw the graph state with Matplotlib. draw_adj(**kwargs) Draw the adjacency matrix with matplotlib. edge_subgraph(edges) Returns the subgraph induced by the specified edges. get_edge_data(u, v[, default]) Returns the attribute dictionary associated with edge (u, v). has_edge(u, v) Returns True if the edge (u, v) is in the graph. Returns True if the graph contains the node n. Generate indices for the nodes of self. Returns True if graph is directed, False otherwise. is_lc_equivalent(graph2[, clifford_form]) Check if two EGraphs are LC equivalent, and return the Clifford operation if so. Returns True if graph is a multigraph, False otherwise. macronize([pad_boundary, disp]) Return a new, macronized version of self. nbunch_iter([nbunch]) Returns an iterator over nodes contained in nbunch that are also in the graph. Returns an iterator over all neighbors of node n. number_of_edges([u, v]) Returns the number of edges between two nodes. Returns the number of nodes in the graph. Returns the number of nodes in the graph. remove_edge(u, v) Remove the edge between u and v. remove_edges_from(ebunch) Remove all edges specified in ebunch. Remove node n. remove_nodes_from(nodes) Remove multiple nodes. remove_qubit(qubit) Remove qubit from EGraph. size([weight]) Returns the number of edges or total of all edge weights. slice_coords(plane, number) Obtain all the coordinates in an x, y, or z slice of self. subgraph(nodes) Returns a SubGraph view of the subgraph induced on nodes. to_directed([as_view]) Returns a directed representation of the graph. Returns the class to use for empty directed copies. to_undirected([as_view]) Returns an undirected copy of the graph. Returns the class to use for empty undirected copies. update([edges, nodes]) Update the graph using nodes/edges/graphs as input.

Add an edge between u and v.

The nodes u and v will be automatically added if they are not already in the graph.

Edge attributes can be specified with keywords or by directly accessing the edge’s attribute dictionary. See examples below.

Parameters
• u_of_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• v_of_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

add_edges_from

Notes

Many NetworkX algorithms designed for weighted graphs use an edge attribute (by default weight) to hold a numerical value.

Examples

The following all add the edge e=(1, 2) to graph G:

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = (1, 2)
>>> G.add_edge(1, 2)  # explicit two-node form
>>> G.add_edge(*e)  # single edge as tuple of two nodes


Associate data to edges using keywords:

>>> G.add_edge(1, 2, weight=3)
>>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7)


For non-string attribute keys, use subscript notation.

>>> G.add_edge(1, 2)
>>> G[1][2].update({0: 5})
>>> G.edges[1, 2].update({0: 5})


Parameters
• ebunch_to_add (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.

• attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

add_edge

add_weighted_edges_from

convenient way to add weighted edges

Notes

Adding the same edge twice has no effect but any edge data will be updated when each duplicate edge is added.

Edge attributes specified in an ebunch take precedence over attributes specified via keyword arguments.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edges_from([(0, 1), (1, 2)])  # using a list of edge tuples
>>> e = zip(range(0, 3), range(1, 4))


Associate data to edges

>>> G.add_edges_from([(1, 2), (2, 3)], weight=3)
>>> G.add_edges_from([(3, 4), (1, 4)], label="WN2898")


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.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> G.number_of_nodes()
3


Use keywords set/change node attributes:

>>> G.add_node(1, size=10)
>>> G.add_node(3, weight=0.4, UTM=("13S", 382871, 3972649))


Notes

A hashable object is one that can be used as a key in a Python dictionary. This includes strings, numbers, tuples of strings and numbers, etc.

On many platforms hashable items also include mutables such as NetworkX Graphs, though one should be careful that the hash doesn’t change on mutables.

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.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> sorted(G.nodes(), key=str)
[0, 1, 2, 'H', 'e', 'l', 'o']


Use keywords to update specific node attributes for every node.

>>> G.add_nodes_from([1, 2], size=10)


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.nodes[1]["size"]
11

add_qubit(qubit: Optional[tuple] = None, neighbors: Optional[list] = None, add_to_macronode: Optional[bool] = None) None[source]

Add qubit to EGraph connected to neighbors.

Parameters
• qubit (tuple[int, int, int] or None) – qubit to add. If a 3-tuple, the qubit is added in that position. If qubit is None, the qubit is positioned one unit further than the maximum position in the x direction, in position (x_max + 1, 0, 0).

• neighbors (list[int], list[tuple], or None) – neighbors of qubit specified with indices or positions.

• add_to_macronode (bool, optional) – if True, add qubit to a macronode. The qubit must be a tuple that rounds to an integer tuple corresponding to the macronode.

Parameters
• ebunch_to_add (container of edges) – Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number.

• weight (string, optional (default= 'weight')) – The attribute name for the edge weights to be added.

• attr (keyword arguments, optional (default= no attributes)) – Edge attributes to add/update for all edges.

add_edge

add_edges_from

Notes

Adding the same edge twice for Graph/DiGraph simply updates the edge data. For MultiGraph/MultiDiGraph, duplicate edges are stored.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)])


Return the correctly indexed adjacency matrix of the graph and set the self.adj_mat attribute.

Calling the NetworkX adjacency matrix methods with default options may create a mismatch between the indices of the rows/columns of the matrix and the indices generated by self.index_generator(). This function demands that the indices match.

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

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]

clear()

Remove all nodes and edges from the graph.

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

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear()
>>> list(G.nodes)
[]
>>> list(G.edges)
[]

clear_edges()

Remove all edges from the graph without altering nodes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear_edges()
>>> list(G.nodes)
[0, 1, 2, 3]
>>> list(G.edges)
[]

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__()


View – Inspired by dict-views, graph-views act like read-only versions of the original graph, providing a copy of the original structure without requiring any memory for copying the information.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Parameters

as_view (bool, optional (default=False)) – If True, the returned graph-view provides a read-only view of the original graph without actually copying any data.

Returns

G – A copy of the graph.

Return type

Graph

to_directed

return a directed copy of the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.copy()

draw(backend='matplotlib', **kwargs)[source]

Draw the graph state with Matplotlib.

See flamingpy.utils.viz.draw_EGraph for more details.

Draw the adjacency matrix with matplotlib.

See flamingpy.utils.viz.plot_mat_heat_map for more details.

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()


Examples

>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]

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
• u (nodes) –

• v (nodes) –

• 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

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0][1]
{}


Warning: Assigning to G[u][v] is not permitted. But it is safe to assign attributes G[u][v][‘foo’]

>>> G[0][1]["weight"] = 7
>>> G[0][1]["weight"]
7
>>> G[1][0]["weight"]
7

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.get_edge_data(0, 1)  # default edge data is {}
{}
>>> e = (0, 1)
>>> G.get_edge_data(*e)  # tuple form
{}
>>> G.get_edge_data("a", "b", default=0)  # edge not in graph, return 0
0

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
• u (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• v (nodes) – 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

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_edge(0, 1)  # using two nodes
True
>>> e = (0, 1)
>>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
True
>>> e = (0, 1, {"weight": 7})
>>> G.has_edge(*e[:2])  # e is a 3-tuple (u, v, data_dictionary)
True


The following syntax are equivalent:

>>> G.has_edge(0, 1)
True
>>> 1 in G[0]  # though this gives KeyError if 0 not in G
True

has_node(n)

Returns True if the graph contains the node n.

Identical to n in G

Parameters

n (node) –

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_node(0)
True


It is more readable and simpler to use

>>> 0 in G
True

index_generator()[source]

Generate indices for the nodes of self.

Set the to_indices and to_points attribute of self with points- to-indices and indices-to-points dictionaries, respectively. Indices are generated using the built-in sorted function (in case of macronodes, the central/integer coordinates are sorted).

is_directed()

Returns True if graph is directed, False otherwise.

is_lc_equivalent(graph2, clifford_form='tensor')[source]

Check if two EGraphs are LC equivalent, and return the Clifford operation if so. Implemented as in arXiv:quant-ph/0405023.

Parameters
• graph2 (EGraph) – the graph to check Clifford equivalence against.

• clifford_form

a string describing the output form of local Clifford operation, if it exists.

If ‘tensor’ (default), produce a list of length n of 2x2 numpy arrays corresponding

to single-qubit tensor factors.

If ‘global’, return a single 2nx2n numpy array corresponding to the global operator

acting on all n qubits.

Returns

whether the states are LC equivalent, and if they are, the local

Clifford output according to ‘clifford_form’ specification.

Return type

(bool, numpy.array)

is_multigraph()

Returns True if graph is a multigraph, False otherwise.

Return a new, macronized version of self.

See egraph.macronize for more details.

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 sequence of nodes. If a node in nbunch is not hashable.

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 all neighbors of node n.

This is identical to iter(G[n])

Parameters

n (node) – A node in the graph

Returns

neighbors – An iterator over all neighbors of node n

Return type

iterator

Raises

NetworkXError – If the node n is not in the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [n for n in G.neighbors(0)]
[1]


Notes

Alternate ways to access the neighbors are G.adj[n] or G[n]:

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G["a"]
AtlasView({'b': {'weight': 7}})
>>> G = nx.path_graph(4)
>>> [n for n in G[0]]
[1]

number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters
• u (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

• v (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

Returns

nedges – 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

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.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

order

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.number_of_nodes()
3

order()

Returns the number of nodes in the graph.

Returns

nnodes – The number of nodes in the graph.

Return type

int

number_of_nodes

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.order()
3

remove_edge(u, v)

Remove the edge between u and v.

Parameters
• u (nodes) – Remove the edge between nodes u and v.

• v (nodes) – Remove the edge between nodes u and v.

Raises

NetworkXError – If there is not an edge between u and v.

remove_edges_from

remove a collection of edges

Examples

>>> G = nx.path_graph(4)  # or DiGraph, etc
>>> G.remove_edge(0, 1)
>>> e = (1, 2)
>>> G.remove_edge(*e)  # unpacks e from an edge tuple
>>> e = (2, 3, {"weight": 7})  # an edge with attribute data
>>> G.remove_edge(*e[:2])  # select first part of edge tuple

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.

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)

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.

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.edges)
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> list(G.edges)
[]

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.

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = list(G.nodes)
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> list(G.nodes)
[]

remove_qubit(qubit: Union[tuple, int]) None[source]

Remove qubit from EGraph.

Parameters

qubit (tuple[int, int, int] or int) – if 3-tuple, remove qubit at that position. If int and index/point dictionary is available, remove qubit at that index.

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

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.size()
3

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.size()
2
>>> G.size(weight="weight")
6.0

slice_coords(plane, number)[source]

Obtain all the coordinates in an x, y, or z slice of self.

Parameters
• plane (str) – ‘x’, ‘y’, or ‘z’, denoting the slice direction

• number (int) – the index of the slice. The allowable range is from 0 to the total number of slices in the given direction.

Returns

the coordinates of the slice.

Return type

list of tuples

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():
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:
for n, nbrs in G.adj.items() if n in largest_wcc
for nbr, d in nbrs.items() if nbr in largest_wcc)
SG.graph.update(G.graph)


Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.subgraph([0, 1, 2])
>>> list(H.edges)
[(0, 1), (1, 2)]

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/3/library/copy.html.

Warning: If you have subclassed Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method.

Examples

>>> G = nx.Graph()  # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]


If already directed, return a (deep) copy

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1)]

to_directed_class()

Returns the class to use for empty directed copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

to_undirected(as_view=False)

Returns an undirected copy of the graph.

Parameters

as_view (bool (optional, default=False)) – If True return a view of the original undirected graph.

Returns

G – A deepcopy of the graph.

Return type

Graph/MultiGraph

Notes

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar G = nx.DiGraph(D) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed DiGraph to use dict-like objects in the data structure, those changes do not transfer to the Graph created by this method.

Examples

>>> G = nx.path_graph(2)  # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]
>>> G2 = H.to_undirected()
>>> list(G2.edges)
[(0, 1)]

to_undirected_class()

Returns the class to use for empty undirected copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

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.

Examples

>>> G = nx.path_graph(5)
>>> G.update(nx.complete_graph(range(4, 10)))
>>> from itertools import combinations
>>> edges = (
...     (u, v, {"power": u * v})
...     for u, v in combinations(range(10, 20), 2)
...     if u * v < 225
... )
>>> nodes = [1000]  # for singleton, use a container
>>> G.update(edges, nodes)


Notes

It you want to update the graph using an adjacency structure it is straightforward to obtain the edges/nodes from adjacency. The following examples provide common cases, your adjacency may be slightly different and require tweaks of these examples:

>>> # dict-of-set/list/tuple
>>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
>>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]

>>> 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()
... ]

>>> # 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()
... ]

>>> # 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()
...     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)


add_edges_from

add multiple edges to a graph

add_nodes_from

add multiple nodes to a graph

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