specless.automaton.product.Product

class specless.automaton.product.Product(nodes: List[Tuple[Hashable, dict]], edges: List[Tuple[Hashable, Hashable, dict]], symbol_display_map: bidict, alphabet_size: int, num_states: int, start_state: Hashable, num_obs: int, final_transition_sym: Hashable, empty_transition_sym: Hashable, is_normalized: bool)[source]

Bases: Automaton

Describes a product automaton between a specification automaton and a dynamics automaton.

You can use this class to compose the two automaton together and then find a controller for the dynamical system that satisfies the specification

param nodes:

node list as expected by networkx.add_nodes_from() (node label, node attribute dict)

param edges:

edge list as expected by networkx.add_edges_from() (src node label, dest node label, edge attribute dict)

param symbol_display_map:

bidirectional mapping of hashable symbols, to a unique integer index in the symbol map. Needed to translate between the indices in the transition distribution and the hashable representation which is meaningful to the user

param alphabet_size:

number of symbols in system alphabet

param num_states:

number of states in automaton state space

param start_state:

unique start state string label of system

param num_obs:

number of observation symbols

param final_transition_sym:

representation of the termination symbol. If not given, will default to base class default.

param empty_transition_sym:

representation of the empty symbol (a.k.a. lambda). If not given, will default to base class default.

param is_normalized:

whether to renormalize the edge probabilities such that each states has a well defined transition probability distribution. We typically DONT want to modify the probabilities of the product algorithm, except if we would like to be able to easily sample traces

Methods

`add_edge`	Add an edge between u and v.
`add_edges_from`	Add all the edges in ebunch_to_add.
`add_node`	Add a single node node_for_adding and update node attributes.
`add_nodes_from`	Add multiple nodes.
`add_weighted_edges_from`	Add weighted edges in ebunch_to_add with specified weight attr
`adjacency`	Returns an iterator over (node, adjacency dict) tuples for all nodes.
`clear`	Remove all nodes and edges from the graph.
`clear_edges`	Remove all edges from the graph without altering nodes.
`compute_strategy`	Calculates a control strategy for the dynamical system that best matches the language of the specification.
`copy`	Returns a copy of the graph.
`disp_edges`	Prints each edge in the graph in an edge-list tuple format
`disp_nodes`	Prints each node's data view
`draw`	Draws (can save) the automaton structure in a way compatible with a jupyter / IPython notebook
`edge_subgraph`	Returns the subgraph induced by the specified edges.
`generate_trace`	Generates a trace w/ prob.
`generate_traces`	Tries to generate num_samples random traces from the product.
`get_edge_data`	Returns the attribute dictionary associated with edge (u, v, key).
`has_edge`	Returns True if the graph has an edge between nodes u and v.
`has_node`	Returns True if the graph contains the node n.
`has_predecessor`	Returns True if node u has predecessor v.
`has_successor`	Returns True if node u has successor v.
`is_directed`	Returns True if graph is directed, False otherwise.
`is_multigraph`	Returns True if graph is a multigraph, False otherwise.
`most_probable_string`	Computes the bounded, most probable string in the probabilistic language of the automaton.
`nbunch_iter`	Returns an iterator over nodes contained in nbunch that are also in the graph.
`neighbors`	Returns an iterator over successor nodes of n.
`new_edge_key`	Returns an unused key for edges between nodes u and v.
`number_of_edges`	Returns the number of edges between two nodes.
`number_of_nodes`	Returns the number of nodes in the graph.
`observe`	Returns the given state's observation symbol
`order`	Returns the number of nodes in the graph.
`plot_node_trans_dist`	Plots the transition pmf at the given curr_state / node.
`predecessors`	Returns an iterator over predecessor nodes of n.
`remove_edge`	Remove an edge between u and v.
`remove_edges_from`	Remove all edges specified in ebunch.
`remove_node`	Remove node n.
`remove_nodes_from`	Remove multiple nodes.
`reverse`	Returns the reverse of the graph.
`size`	Returns the number of edges or total of all edge weights.
`subgraph`	Returns a SubGraph view of the subgraph induced on nodes.
`successors`	Returns an iterator over successor nodes of n.
`to_directed`	Returns a directed representation of the graph.
`to_directed_class`	Returns the class to use for empty directed copies.
`to_undirected`	Returns an undirected representation of the digraph.
`to_undirected_class`	Returns the class to use for empty undirected copies.
`update`	Update the graph using nodes/edges/graphs as input.
`write_traces_to_file`	Writes trace samples to a file in the abbadingo format for use in grammatical inference tools like flexfringe

Attributes

`adj`	Graph adjacency object holding the neighbors of each node.
`automata_data_dir`
`automata_display_data_dir_name`
`degree`	A DegreeView for the Graph as G.degree or G.degree().
`edges`	An OutMultiEdgeView of the Graph as G.edges or G.edges().
`in_degree`	A DegreeView for (node, in_degree) or in_degree for single node.
`in_edges`	A view of the in edges of the graph as G.in_edges or G.in_edges().
`name`	String identifier of the graph.
`nodes`	A NodeView of the Graph as G.nodes or G.nodes().
`out_degree`	Returns an iterator for (node, out-degree) or out-degree for single node.
`out_edges`	An OutMultiEdgeView of the Graph as G.edges or G.edges().
`pred`	Graph adjacency object holding the predecessors of each node.
`succ`	Graph adjacency object holding the successors of each node.
`alphabet_size`	number of symbols in automaton alphabet
`num_states`	number of states in automaton state space
`num_obs`	number of state observations in TS obs.
`final_transition_sym`	representation of the termination symbol
`empty_transition_sym`	symbol to use as the empty (a.k.a.
`start_state`	unique start state string label of automaton
`is_stochastic`	whether symbol probabilities are given for string generation
`is_sampleable`	transitions will have pre-computed, well-formed distributions
`is_normalized`	ill-defined transition distributions are normalized to be proper probability distributions over outgoing transitions
`symbols`	set of all symbols used by the automaton
`state_labels`	set of all states in the automaton
`observations`	the set of all possible state output symbols (observations)
`is_deterministic`	whether or not there is a unique state dest.

add_edge(u_for_edge, v_for_edge, key=None, **attr)

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_for_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.
v_for_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.
key (hashable identifier, optional (default=lowest unused integer)) – Used to distinguish multiedges between a pair of nodes.
attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

Return type:

The edge key assigned to the edge.

See also

add_edges_from: add a collection of edges

Notes

To replace/update edge data, use the optional key argument to identify a unique edge. Otherwise a new edge will be created.

NetworkX algorithms designed for weighted graphs cannot use multigraphs directly because it is not clear how to handle multiedge weights. Convert to Graph using edge attribute ‘weight’ to enable weighted graph algorithms.

Default keys are generated using the method new_edge_key(). This method can be overridden by subclassing the base class and providing a custom new_edge_key() method.

Examples

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

>>> G = nx.MultiDiGraph()
>>> e = (1, 2)
>>> key = G.add_edge(1, 2)  # explicit two-node form
>>> G.add_edge(*e)  # single edge as tuple of two nodes
1
>>> G.add_edges_from([(1, 2)])  # add edges from iterable container
[2]

Associate data to edges using keywords:

>>> key = G.add_edge(1, 2, weight=3)
>>> key = G.add_edge(1, 2, key=0, weight=4)  # update data for key=0
>>> key = G.add_edge(1, 3, weight=7, capacity=15, length=342.7)

For non-string attribute keys, use subscript notation.

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

add_edges_from(ebunch_to_add, **attr)

Add all the edges in ebunch_to_add.

Parameters:

ebunch_to_add (container of edges) –
Each edge given in the container will be added to the graph. The edges can be:
- 2-tuples (u, v) or
- 3-tuples (u, v, d) for an edge data dict d, or
- 3-tuples (u, v, k) for not iterable key k, or
- 4-tuples (u, v, k, d) for an edge with data and key k
attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

Return type:

A list of edge keys assigned to the edges in ebunch.

See also

add_edge: add a single 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.

Default keys are generated using the method new_edge_key(). This method can be overridden by subclassing the base class and providing a custom new_edge_key() method.

When adding edges from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_edges), and pass this object to G.add_edges_from.

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))
>>> G.add_edges_from(e)  # Add the path graph 0-1-2-3

Associate data to edges

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

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.MultiGraph([(1, 2), (2, 3), (3, 4)])
>>> # Grow graph by one new node, adding edges to all existing nodes.
>>> # wrong way - will raise RuntimeError
>>> # G.add_edges_from(((5, n) for n in G.nodes))
>>> # right way - note that there will be no self-edge for node 5
>>> assigned_keys = G.add_edges_from(list((5, n) for n in G.nodes))

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

Examples

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

Use keywords set/change node attributes:

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

Notes

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

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

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

Notes

When adding nodes from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_nodes), and pass this object to G.add_nodes_from.

Examples

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

Use keywords to update specific node attributes for every node.

>>> G.add_nodes_from([1, 2], size=10)
>>> G.add_nodes_from([3, 4], weight=0.4)

Use (node, attrdict) tuples to update attributes for specific nodes.

>>> G.add_nodes_from([(1, dict(size=11)), (2, {"color": "blue"})])
>>> G.nodes[1]["size"]
11
>>> H = nx.Graph()
>>> H.add_nodes_from(G.nodes(data=True))
>>> H.nodes[1]["size"]
11

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(0, 1), (1, 2), (3, 4)])
>>> # wrong way - will raise RuntimeError
>>> # G.add_nodes_from(n + 1 for n in G.nodes)
>>> # correct way
>>> G.add_nodes_from(list(n + 1 for n in G.nodes))

add_weighted_edges_from(ebunch_to_add, weight='weight', **attr)

Add weighted edges in ebunch_to_add with specified weight attr

Parameters:

ebunch_to_add (container of edges) – Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number.
weight (string, optional (default= 'weight')) – The attribute name for the edge weights to be added.
attr (keyword arguments, optional (default= no attributes)) – Edge attributes to add/update for all edges.

See also

add_edge: add a single edge
add_edges_from: add multiple edges

Notes

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

When adding edges from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_edges), and pass this object to G.add_weighted_edges_from.

Examples

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

Evaluate an iterator over edges before passing it

>>> G = nx.Graph([(1, 2), (2, 3), (3, 4)])
>>> weight = 0.1
>>> # Grow graph by one new node, adding edges to all existing nodes.
>>> # wrong way - will raise RuntimeError
>>> # G.add_weighted_edges_from(((5, n, weight) for n in G.nodes))
>>> # correct way - note that there will be no self-edge for node 5
>>> G.add_weighted_edges_from(list((5, n, weight) for n in G.nodes))

property 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 edgekey-dict. So G.adj[3][2][0][‘color’] = ‘blue’ sets the color of the edge (3, 2, 0) 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

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: {}})]

adjlist_inner_dict_factory: alias of dict

adjlist_outer_dict_factory: alias of dict

alphabet_size: number of symbols in automaton alphabet

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)
[]

compute_strategy(min_string_probability: {None, <class 'float'>} = None, max_string_length: {None, <class 'int'>} = None) → Tuple[Iterable[Hashable], float][source]

Calculates a control strategy for the dynamical system that best matches the language of the specification.

Parameters:

min_string_probability – The minimum string probability
max_string_length – The maximum string length

Returns:

The sequence of controls to apply, the probability in the languge of the specification of generating the output word of the dynamical system under the control symbols.

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/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

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()

property 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 DiMultiDegreeView mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer.

Return type:

DiMultiDegreeView or int

See also

out_degree, in_degree

Examples

>>> G = nx.MultiDiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.degree(0)  # node 0 with degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]
>>> G.add_edge(0, 1) # parallel edge
1
>>> list(G.degree([0, 1, 2])) # parallel edges are counted
[(0, 2), (1, 3), (2, 2)]

disp_edges(graph: {None, <class 'networkx.classes.multidigraph.MultiDiGraph'>} = None) → None

Prints each edge in the graph in an edge-list tuple format

Parameters:: graph ({None, nx.MultiDiGraph}) – The graph to access. Default = None => use instance

disp_nodes(graph: {None, <class 'networkx.classes.multidigraph.MultiDiGraph'>} = None) → None

Prints each node’s data view

Parameters:: graph ({None, nx.MultiDiGraph}) – The graph to access. Default = None => use instance

draw(filename: {None, <class 'str'>} = None, should_display: bool = True, img_format='png') → None

Draws (can save) the automaton structure in a way compatible with a jupyter / IPython notebook

Parameters:: filename – The filename to save the automaton image

edge_attr_dict_factory: alias of dict

edge_key_dict_factory: alias of 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()

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)]

property edges

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

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

The OutMultiEdgeView 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, k]['color'] provides the value of the color attribute for the edge from u to v with key k while for (u, v, k, c) in G.edges(data='color', default='red', keys=True): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Edges are returned as tuples with optional data and keys in the order (node, neighbor, key, data). If keys=True is not provided, the tuples will just be (node, neighbor, data), but multiple tuples with the same node and neighbor will be generated when multiple edges between two nodes exist.

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).
keys (bool, optional (default=False)) – If True, return edge keys with each edge, creating (u, v, k, d) tuples when data is also requested (the default) and (u, v, k) tuples when data is not requested.
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) (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'].

Return type:

OutMultiEdgeView

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.MultiDiGraph()
>>> nx.add_path(G, [0, 1, 2])
>>> key = G.add_edge(2, 3, weight=5)
>>> key2 = G.add_edge(1, 2) # second edge between these nodes
>>> [e for e in G.edges()]
[(0, 1), (1, 2), (1, 2), (2, 3)]
>>> list(G.edges(data=True))  # default data is {} (empty dict)
[(0, 1, {}), (1, 2, {}), (1, 2, {}), (2, 3, {'weight': 5})]
>>> list(G.edges(data="weight", default=1))
[(0, 1, 1), (1, 2, 1), (1, 2, 1), (2, 3, 5)]
>>> list(G.edges(keys=True))  # default keys are integers
[(0, 1, 0), (1, 2, 0), (1, 2, 1), (2, 3, 0)]
>>> list(G.edges(data=True, keys=True))
[(0, 1, 0, {}), (1, 2, 0, {}), (1, 2, 1, {}), (2, 3, 0, {'weight': 5})]
>>> list(G.edges(data="weight", default=1, keys=True))
[(0, 1, 0, 1), (1, 2, 0, 1), (1, 2, 1, 1), (2, 3, 0, 5)]
>>> list(G.edges([0, 2]))
[(0, 1), (2, 3)]
>>> list(G.edges(0))
[(0, 1)]
>>> list(G.edges(1))
[(1, 2), (1, 2)]

See also

in_edges, out_edges

empty_transition_sym: symbol to use as the empty (a.k.a. lambda) symbol

final_transition_sym: representation of the termination symbol

generate_trace(start_state: ~typing.Hashable, N: int, max_resamples: int = 10, return_whatever_you_got: bool = False, random_state: {None, <class 'int'>, typing.Iterable} = None) -> (typing.Iterable[typing.Hashable], <class 'int'>, <class 'float'>)

Generates a trace w/ prob. > 0 from the automaton from its start_state

Parameters:

start_state – the state label to start sampling traces from
N – maximum length of trace
max_resamples – The maximum number of times to resample if if we create a trace of length N that still doesn’t have a probability > 0 in the language
return_whatever_you_got – Whether to return a string with a zero probability after all resampling attempts are exhausted.
random_state – The np.random.RandomState() seed parameter for sampling from the state transition distribution. Defaulting to None causes the seed to reset.

Returns:

the sequence of symbols emitted, the length of the trace, the probability of the trace in the language of the automaton

Raises:

ValueError – if you try to generate a trace from a non-sampleable automaton

generate_traces(num_samples: int, N: int | None = None, num_traces_to_find: int | None = None, min_trace_probability: float | None = None, complete_samples: bool = False, max_resamples: int = 100, use_greedy_MPS_sampler: bool = True, force_MPS_sampler: bool = False, return_whatever_you_got: bool = False, force_multicore: bool = True, show_progress_bar: bool = True)[source]

Tries to generate num_samples random traces from the product.

Parameters:

num_samples – The number of trace samples to generate
N – maximum length of any trace
num_traces_to_find – the number of base random traces to find in the automaton when using the MPS sampler. This is not necessarily the same as num_samples, as often the MPS sampler is too slow to return that many samples. Thus, if you allow for it, the MPS samples can be resampled to return num_samples samples after the MPS sampler is done.
min_trace_probability – The minimum trace probability. only needed when using the MPS sampler. Lowering this will result in more random (less representative traces), but will make the algorithm much faster. If set TOO high, you will find no traces meeting this requirement. (default 0.0)
complete_samples – If enabled, if the underlying sampler fails to generate num_samples, then any samples it does find will be resampled to create num_samples samples occurring with correct RELATIVE frequencies.
max_resamples – The maximum number of times to resample if if we create a trace of length N that still doesn’t have a probability > 0 in the language
use_greedy_MPS_sampler – whether to try using the MUCH faster greedy search algorithm. only possible if the automaton has deterministic transitions. Only set this to False if the automaton actually is non-deterministic, as the non-deterministic solver is an approximation and MUCH slower.
force_MPS_sampler – by default, IF THE PRODUCT HAS BEEN NORMALIZED (and thus is sampleable), then it will fall back on the base class’ sampler. Not available if the product is not is_sampleable. This sampler is truly a random MC sampler, and thus is appropriate if you want to generate traces with more randomness than the MPS sampler.
return_whatever_you_got – Whether to return a string with a zero probability after all resampling attempts are exhausted.
force_multicore – whether to force use the threaded sampler this is set by default to optimize speed, as the threaded sampler is slower for smaller num_samples. Force this to be true if the automaton is slow to sample.
show_progress_bar – whether to show a tqdm progress bar for each sampled trace. Only turn this on if you’re sampling a few traces from a very expensive-to-sample automaton.

Returns:

list of sampled traces, list of the associated trace lengths, list of the associated trace probabilities

Return type:

tuple(list(list(int)), list(int), list(float))

get_edge_data(u, v, key=None, default=None)

Returns the attribute dictionary associated with edge (u, v, key).

If a key is not provided, returns a dictionary mapping edge keys to attribute dictionaries for each edge between u and 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 (nodes) –
v (nodes) –
default (any Python object (default=None)) – Value to return if the specific edge (u, v, key) is not found, OR if there are no edges between u and v and no key is specified.
key (hashable identifier, optional (default=None)) – Return data only for the edge with specified key, as an attribute dictionary (rather than a dictionary mapping keys to attribute dictionaries).

Returns:

edge_dict – The edge attribute dictionary, OR a dictionary mapping edge keys to attribute dictionaries for each of those edges if no specific key is provided (even if there’s only one edge between u and v).

Return type:

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.edges[0, 1, 0]["weight"] = 5
>>> G.get_edge_data(0, 1)
{0: {'weight': 5}}
>>> e = (0, 1)
>>> G.get_edge_data(*e)  # tuple form
{0: {'weight': 5}}
>>> G.get_edge_data(3, 0)  # edge not in graph, returns None
>>> G.get_edge_data(3, 0, default=0)  # edge not in graph, return default
0
>>> G.get_edge_data(1, 0, 0)  # specific key gives back
{'weight': 5}

graph_attr_dict_factory: alias of dict

has_edge(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 (nodes) – Nodes can be, for example, strings or numbers.
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 – True if edge is in the graph, False otherwise.

Return type:

bool

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
>>> G.has_edge(1, 0, key="a")  # edges aren't directed
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
>>> 0 in G[1]  # other order; also gives :exc:`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

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.

property in_degree

A DegreeView for (node, in_degree) or in_degree for single node.

The node in-degree is the number of edges pointing in 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 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, in-degree).

See also

degree, out_degree

Examples

>>> G = nx.MultiDiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.in_degree(0)  # node 0 with degree 0
0
>>> list(G.in_degree([0, 1, 2]))
[(0, 0), (1, 1), (2, 1)]
>>> G.add_edge(0, 1) # parallel edge
1
>>> list(G.in_degree([0, 1, 2])) # parallel edges counted
[(0, 0), (1, 2), (2, 1)]

property in_edges

A view of the in edges of the graph as G.in_edges or G.in_edges().

in_edges(self, nbunch=None, data=False, keys=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).
keys (bool, optional (default=False)) – If True, return edge keys with each edge, creating 3-tuples (u, v, k) or with data, 4-tuples (u, v, k, d).
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, k) or (u, v, k, d) tuples of edges, but can also be used for attribute lookup as edges[u, v, k][‘foo’].

Return type:

InMultiEdgeView or InMultiEdgeDataView

See also

edges

is_deterministic: whether or not there is a unique state dest. under each symbol. Defaults to true and is falsified later during initialization.

is_directed(): Returns True if graph is directed, False otherwise.

is_multigraph(): Returns True if graph is a multigraph, False otherwise.

is_normalized: ill-defined transition distributions are normalized to be proper probability distributions over outgoing transitions

is_sampleable: transitions will have pre-computed, well-formed distributions

is_stochastic: whether symbol probabilities are given for string generation

most_probable_string(min_string_probability: {None, <class 'float'>} = None, max_string_length: {None, <class 'int'>} = None, allow_empty_symbol: bool = False, try_to_use_greedy: bool = True, backwards_search: bool = True, num_strings_to_find: int = 1, depth_first: bool = False, add_entropy: bool = False, disable_pbar: bool = False) → Tuple[Iterable[Hashable], float, List[Tuple[float, Tuple[Iterable[Hashable], Iterable[float]]]]]

Computes the bounded, most probable string in the probabilistic language of the automaton.

Parameters:

min_string_probability – The minimum string probability. This setting does nothing if is_deterministic, as the deterministic algorithm is exact. (default 0.0)
max_string_length – The maximum string length. This setting does nothing if is_deterministic, as the deterministic algorithm is exact. (default 100)
allow_empty_symbol – Indicates if the empty symbol is allowed
try_to_use_greedy – whether to try using the MUCH faster greedy search algorithm. only possible if the automaton has deterministic transitions. Only set this to False if the automaton actually is non-deterministic, as the non-deterministic solver is an approximation and MUCH slower.
backwards_search – Whether to search from the with final probability back to the start state. Often will improve performance.
num_strings_to_find – The number of viable strings to return. Defaults to only return the ONE, highest probability string encountered thus far in the search, which means the algorithm is the original BMPS_exact. If >1, then the algorithm returns the num_strings_to_find most probable, viable strings from the search heap.
depth_first – Whether to explore the automaton using a depth-first search pattern. Using a depth-first search pattern will be faster for very deep, tree-shaped automaton, but will not return the absolute best symbol sequence for the given min_string_prob and max_string_length. Only turn on if you have a terminal states deep in the automaton and you need the search to be faster.
add_entropy – Only keeps a new viable string if it has a previously unseen probability of being generated
disable_pbar – Disable pbar for speeding up the computation speed.

Returns:

most probable string, probability of producing the most probable string, num_strings_to_find (their probs., viable strings) ranked by each string’s probability.

Raises:

ValueError – Cannot be computed for non-stochastic automaton

property 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 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.

new_edge_key(u, v)

Returns an unused key for edges between nodes u and v.

The nodes u and v do not need to be already in the graph.

Notes

In the standard MultiGraph class the new key is the number of existing edges between u and v (increased if necessary to ensure unused). The first edge will have key 0, then 1, etc. If an edge is removed further new_edge_keys may not be in this order.

Parameters:

u (nodes) –
v (nodes) –

Returns:

key

Return type:

int

node_attr_dict_factory: alias of dict

node_dict_factory: alias of dict

property 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}

num_obs: number of state observations in TS obs. space

num_states: number of states in automaton state space

number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters:

u (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.
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 – 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 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

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: identical method
__len__: identical method

Examples

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

observations: the set of all possible state output symbols (observations)

observe(curr_state: Hashable) → Hashable[source]

Returns the given state’s observation symbol

Parameters:: curr_state – The current product state
Returns:: observation symbol emitted at curr_state

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: identical method
__len__: identical method

Examples

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

property out_degree

Returns an iterator for (node, out-degree) or out-degree for single node.

out_degree(self, nbunch=None, weight=None)

The node out-degree is the number of edges pointing out of the node. This function returns the out-degree for a single node or an iterator for a bunch of nodes or if nothing is passed as argument.

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 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.

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, out-degree).

See also

degree, in_degree

Examples

>>> G = nx.MultiDiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.out_degree(0)  # node 0 with degree 1
1
>>> list(G.out_degree([0, 1, 2]))
[(0, 1), (1, 1), (2, 1)]
>>> G.add_edge(0, 1) # parallel edge
1
>>> list(G.out_degree([0, 1, 2])) # counts parallel edges
[(0, 2), (1, 1), (2, 1)]

property out_edges

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

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

The OutMultiEdgeView 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, k]['color'] provides the value of the color attribute for the edge from u to v with key k while for (u, v, k, c) in G.edges(data='color', default='red', keys=True): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Edges are returned as tuples with optional data and keys in the order (node, neighbor, key, data). If keys=True is not provided, the tuples will just be (node, neighbor, data), but multiple tuples with the same node and neighbor will be generated when multiple edges between two nodes exist.

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).
keys (bool, optional (default=False)) – If True, return edge keys with each edge, creating (u, v, k, d) tuples when data is also requested (the default) and (u, v, k) tuples when data is not requested.
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) (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'].

Return type:

OutMultiEdgeView

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.MultiDiGraph()
>>> nx.add_path(G, [0, 1, 2])
>>> key = G.add_edge(2, 3, weight=5)
>>> key2 = G.add_edge(1, 2) # second edge between these nodes
>>> [e for e in G.edges()]
[(0, 1), (1, 2), (1, 2), (2, 3)]
>>> list(G.edges(data=True))  # default data is {} (empty dict)
[(0, 1, {}), (1, 2, {}), (1, 2, {}), (2, 3, {'weight': 5})]
>>> list(G.edges(data="weight", default=1))
[(0, 1, 1), (1, 2, 1), (1, 2, 1), (2, 3, 5)]
>>> list(G.edges(keys=True))  # default keys are integers
[(0, 1, 0), (1, 2, 0), (1, 2, 1), (2, 3, 0)]
>>> list(G.edges(data=True, keys=True))
[(0, 1, 0, {}), (1, 2, 0, {}), (1, 2, 1, {}), (2, 3, 0, {'weight': 5})]
>>> list(G.edges(data="weight", default=1, keys=True))
[(0, 1, 0, 1), (1, 2, 0, 1), (1, 2, 1, 1), (2, 3, 0, 5)]
>>> list(G.edges([0, 2]))
[(0, 1), (2, 3)]
>>> list(G.edges(0))
[(0, 1)]
>>> list(G.edges(1))
[(1, 2), (1, 2)]

See also

in_edges, out_edges

plot_node_trans_dist(curr_state: Hashable) → None

Plots the transition pmf at the given curr_state / node.

Parameters:: curr_state (Hashable) – state to display its transition distribution

property 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 edgekey-dict. So G.adj[3][2][0][‘color’] = ‘blue’ sets the color of the edge (3, 2, 0) to “blue”.

Iterating over G.adj behaves like a dict. Useful idioms include for nbr, datadict in G.adj[n].items():.

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, key=None)

Remove an edge between u and v.

Parameters:

u (nodes) – Remove an edge between nodes u and v.
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 edge between u and v. If there are multiple edges, removes the last edge added in terms of insertion order.

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.MultiDiGraph()
>>> 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.MultiDiGraph()
>>> G.add_edges_from([(1, 2), (1, 2), (1, 2)])  # key_list returned
[0, 1, 2]

When key=None (the default), edges are removed in the opposite order that they were added:

>>> G.remove_edge(1, 2)
>>> G.edges(keys=True)
OutMultiEdgeView([(1, 2, 0), (1, 2, 1)])

For edges with keys

>>> G = nx.MultiDiGraph()
>>> G.add_edge(1, 2, key="first")
'first'
>>> G.add_edge(1, 2, key="second")
'second'
>>> G.remove_edge(1, 2, key="first")
>>> G.edges(keys=True)
OutMultiEdgeView([(1, 2, 'second')])

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) A single edge between u and v is 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), (2, 1)])  # edges aren't directed
>>> list(G.edges())
[(1, 2)]
>>> G.remove_edges_from([(1, 2), (1, 2)])  # silently ignore extra copy
>>> list(G.edges)  # now empty graph
[]

When the edge is a 2-tuple (u, v) but there are multiple edges between u and v in the graph, the most recent edge (in terms of insertion order) is removed.

>>> G = nx.MultiGraph()
>>> for key in ("x", "y", "a"):
...     k = G.add_edge(0, 1, key=key)
>>> G.edges(keys=True)
MultiEdgeView([(0, 1, 'x'), (0, 1, 'y'), (0, 1, 'a')])
>>> G.remove_edges_from([(0, 1)])
>>> G.edges(keys=True)
MultiEdgeView([(0, 1, 'x'), (0, 1, 'y')])

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.

See also

remove_nodes_from

Examples

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

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

Notes

When removing nodes from an iterator over the graph you are changing, a RuntimeError will be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_nodes), and pass this object to G.remove_nodes_from.

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)
[]

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(0, 1), (1, 2), (3, 4)])
>>> # this command will fail, as the graph's dict is modified during iteration
>>> # G.remove_nodes_from(n for n in G.nodes if n < 2)
>>> # this command will work, since the dictionary underlying graph is not modified
>>> G.remove_nodes_from(list(n for n in G.nodes if n < 2))

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

See also

number_of_edges

Examples

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

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge("a", "b", weight=2)
>>> G.add_edge("b", "c", weight=4)
>>> G.size()
2
>>> G.size(weight="weight")
6.0

start_state: unique start state string label of automaton

state_labels: set of all states in the automaton

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)

Examples

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

property 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 edgekey-dict. So G.adj[3][2][0][‘color’] = ‘blue’ sets the color of the edge (3, 2, 0) 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.succ is identical to G.adj.

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.

symbols: set of all symbols used by the automaton

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, k, data) replaced by two directed edges (u, v, k, data) and (v, u, k, data).
Return type:: MultiDiGraph

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=MultiDiGraph(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 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.MultiGraph()
>>> G.add_edge(0, 1)
0
>>> G.add_edge(0, 1)
1
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1)]

If already directed, return a (deep) copy

>>> G = nx.MultiDiGraph()
>>> G.add_edge(0, 1)
0
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1, 0)]

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(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:

MultiGraph

See also

MultiGraph, 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 D=MultiDiGraph(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 MultiDiGraph 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)]

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]
>>> 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

classmethod write_traces_to_file(traces: ~typing.List[~typing.Iterable[~typing.Hashable]], file: str, alphabet_size: int, base_file_dir: {None, <class 'str'>} = None) → str

Writes trace samples to a file in the abbadingo format for use in grammatical inference tools like flexfringe

Parameters:

traces – The traces to write to a file
file – The file name to write to. Can be a partial path.
alphabet_size – The alphabet size
base_file_dir – Provide this if you want to output the file to a different location than self.automata_data_dir.

Returns:

the absolute filepath to the traces. Will be: abs_filepath(self.automata_data_dir/file) if base_file_dir is None. Else, will be: abs_filepath(base_file_dir/file)