Graph Module

PyBNesian includes different types of graphs. There are four types of graphs:

• Undirected graphs.

• Directed graphs.

• Directed acyclic graphs (DAGs).

• Partially directed graphs.

Depending on the type of edges: directed edges (arcs) or undirected edges (edges).

Each graph type has two variants:

• Graphs. See Graphs.

• Conditional graphs. See Conditional Graphs.

Graphs

All the nodes in the graph are represented by a name and are associated with a non-negative unique index.

The name can be obtained from the unique index using the method name(), while the unique index can be obtained from the index using the method index().

Removing a node invalidates the index of the removed node, while leaving the other nodes unaffected. When adding a node, the graph may reuse previously invalidated indices to avoid wasting too much memory.

If there are not removal of nodes in a graph, the unique indices are in the range [0-num_nodes()). The removal of nodes, can lead to some indices being greater or equal to num_nodes():

>>> from pybnesian import UndirectedGraph
>>> g = UndirectedGraph(["a", "b", "c", "d"])
>>> g.index("a")
0
>>> g.index("b")
1
>>> g.index("c")
2
>>> g.index("d")
3
>>> g.remove_node("a")
>>> g.index("b")
1
>>> g.index("c")
2
>>> g.index("d")
3
>>> assert g.index("d") >= g.num_nodes()

Sometimes, this effect may be undesirable because we want to identify our nodes with a index in a range [0-num_nodes()). For this reason, there is a collapsed_index() method and other related methods index_from_collapsed(), collapsed_from_index() and collapsed_name(). Note that the collapsed index is not unique, because removing a node can change the collapsed index of at most one other node.

>>> from pybnesian import UndirectedGraph
>>> g = UndirectedGraph(["a", "b", "c", "d"])
>>> g.collapsed_index("a")
0
>>> g.collapsed_index("b")
1
>>> g.collapsed_index("c")
2
>>> g.collapsed_index("d")
3
>>> g.remove_node("a")
>>> g.collapsed_index("b")
1
>>> g.collapsed_index("c")
2
>>> g.collapsed_index("d")
0
>>> assert all([g.collapsed_index(n) < g.num_nodes() for n in g.nodes()])

class pybnesian.UndirectedGraph

Undirected graph.

static Complete(nodes: list[str]) → pybnesian.UndirectedGraph

Creates a complete UndirectedGraph with the specified nodes.

Parameters:

nodes – Nodes of the UndirectedGraph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.UndirectedGraph) -> None

Creates a UndirectedGraph without nodes or edges.

2. __init__(self: pybnesian.UndirectedGraph, nodes: list[str]) -> None

Creates an UndirectedGraph with the specified nodes and without edges.

Parameters:

nodes – Nodes of the UndirectedGraph.

3. __init__(self: pybnesian.UndirectedGraph, edges: list[tuple[str, str]]) -> None

Creates an UndirectedGraph with the specified edges (the nodes are extracted from the edges).

Parameters:

edges – Edges of the UndirectedGraph.

4. __init__(self: pybnesian.UndirectedGraph, nodes: list[str], edges: list[tuple[str, str]]) -> None

Creates an UndirectedGraph with the specified nodes and edges.

Parameters:

• nodes – Nodes of the UndirectedGraph.

• edges – Edges of the UndirectedGraph.

add_edge(self: pybnesian.UndirectedGraph, n1: int or str, n2: int or str) → None

Adds an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

add_node(self: pybnesian.UndirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

collapsed_from_index(self: pybnesian.UndirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.UndirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.UndirectedGraph) → dict[str, int]

Gets the collapsed indices in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.UndirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.UndirectedGraph) -> pybnesian.ConditionalUndirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.UndirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalUndirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_node(self: pybnesian.UndirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

edges(self: pybnesian.UndirectedGraph) → list[tuple[str, str]]

Gets the list of edges.

Returns:

A list of tuples (n1, n2) representing an edge between n1 and n2.

has_edge(self: pybnesian.UndirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether an edge between the nodes n1 and n2 exists.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if the edge exists, False otherwise.

has_path(self: pybnesian.UndirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether there is an undirected path between nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if there is an undirected path between n1 and n2, False otherwise.

index(self: pybnesian.UndirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.UndirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.UndirectedGraph) → dict[str, int]

Gets all the indices in the graph.

Returns:

A dictionary with the index of each node.

is_valid(self: pybnesian.UndirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

name(self: pybnesian.UndirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

neighbors(self: pybnesian.UndirectedGraph, node: int or str) → List[str]

Gets the neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Neighbor names.

nodes(self: pybnesian.UndirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_edges(self: pybnesian.UndirectedGraph) → int

Gets the number of edges.

Returns:

Number of edges.

num_neighbors(self: pybnesian.UndirectedGraph, node: int or str) → int

Gets the number of neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Number of neighbors.

num_nodes(self: pybnesian.UndirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

remove_edge(self: pybnesian.UndirectedGraph, n1: int or str, n2: int or str) → None

Removes an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

remove_node(self: pybnesian.UndirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

save(self: pybnesian.UndirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

unconditional_graph(self: pybnesian.UndirectedGraph) → pybnesian.UndirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.DirectedGraph

Directed graph that may contain cycles.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.DirectedGraph) -> None

Creates a DirectedGraph without nodes or arcs.

2. __init__(self: pybnesian.DirectedGraph, nodes: list[str]) -> None

Creates a DirectedGraph with the specified nodes and without arcs.

Parameters:

nodes – Nodes of the DirectedGraph.

3. __init__(self: pybnesian.DirectedGraph, arcs: list[tuple[str, str]]) -> None

Creates a DirectedGraph with the specified arcs (the nodes are extracted from the arcs).

Parameters:

arcs – Arcs of the DirectedGraph.

4. __init__(self: pybnesian.DirectedGraph, nodes: list[str], arcs: list[tuple[str, str]]) -> None

Creates a DirectedGraph with the specified nodes and arcs.

Parameters:

• nodes – Nodes of the DirectedGraph.

• arcs – Arcs of the DirectedGraph.

add_arc(self: pybnesian.DirectedGraph, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

add_node(self: pybnesian.DirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

arcs(self: pybnesian.DirectedGraph) → list[tuple[str, str]]

Gets the list of arcs.

Returns:

A list of tuples (source, target) representing an arc source -> target.

children(self: pybnesian.DirectedGraph, node: int or str) → List[str]

Gets the children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Children node names.

collapsed_from_index(self: pybnesian.DirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.DirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.DirectedGraph) → dict[str, int]

Gets the collapsed indices in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.DirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.DirectedGraph) -> pybnesian.ConditionalDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.DirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_node(self: pybnesian.DirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

flip_arc(self: pybnesian.DirectedGraph, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

has_arc(self: pybnesian.DirectedGraph, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target exists.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc exists, False otherwise.

has_path(self: pybnesian.DirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether there is a directed path between nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if there is an directed path between n1 and n2, False otherwise.

index(self: pybnesian.DirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.DirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.DirectedGraph) → dict[str, int]

Gets all the indices in the graph.

Returns:

A dictionary with the index of each node.

is_leaf(self: pybnesian.DirectedGraph, node: int or str) → bool

Checks whether node is a leaf node. A root node do not have children nodes.

Parameters:

node – A node name or index.

Returns:

True if node is leaf, False otherwise.

is_root(self: pybnesian.DirectedGraph, node: int or str) → bool

Checks whether node is a root node. A root node do not have parent nodes.

Parameters:

node – A node name or index.

Returns:

True if node is root, False otherwise.

is_valid(self: pybnesian.DirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

leaves(self: pybnesian.DirectedGraph) → set[str]

Gets the leaf nodes of the graph. A leaf node do not have children nodes.

Returns:

The set of leaf nodes.

name(self: pybnesian.DirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

nodes(self: pybnesian.DirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_arcs(self: pybnesian.DirectedGraph) → int

Gets the number of arcs.

Returns:

Number of arcs.

num_children(self: pybnesian.DirectedGraph, node: int or str) → int

Gets the number of children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of children nodes.

num_nodes(self: pybnesian.DirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

num_parents(self: pybnesian.DirectedGraph, node: int or str) → int

Gets the number of parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of parent nodes.

parents(self: pybnesian.DirectedGraph, node: int or str) → List[str]

Gets the parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Parent node names.

remove_arc(self: pybnesian.DirectedGraph, source: int or str, target: int or str) → None

Removes an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

remove_node(self: pybnesian.DirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

roots(self: pybnesian.DirectedGraph) → set[str]

Gets the root nodes of the graph. A root node do not have parent nodes.

Returns:

The set of root nodes.

save(self: pybnesian.DirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

unconditional_graph(self: pybnesian.DirectedGraph) → pybnesian.DirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.Dag

Bases: DirectedGraph

Directed acyclic graph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.Dag) -> None

Creates a Dag without nodes or arcs.

2. __init__(self: pybnesian.Dag, nodes: list[str]) -> None

Creates a Dag with the specified nodes and without arcs.

Parameters:

nodes – Nodes of the Dag.

3. __init__(self: pybnesian.Dag, arcs: list[tuple[str, str]]) -> None

Creates a Dag with the specified arcs (the nodes are extracted from the arcs).

Parameters:

arcs – Arcs of the Dag.

4. __init__(self: pybnesian.Dag, nodes: list[str], arcs: list[tuple[str, str]]) -> None

Creates a Dag with the specified nodes and arcs.

Parameters:

• nodes – Nodes of the Dag.

• arcs – Arcs of the Dag.

add_arc(self: pybnesian.Dag, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

can_add_arc(self: pybnesian.Dag, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target can be added. That is, the arc is valid and do not generate a cycle.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc can be added, False otherwise.

can_flip_arc(self: pybnesian.Dag, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target can be flipped. That is, the flipped arc is valid and do not generate a cycle. If the arc source -> target do not exist, it will return Dag.can_add_arc().

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc can be flipped, False otherwise.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.Dag) -> pybnesian.ConditionalDag

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.Dag, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalDag

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

flip_arc(self: pybnesian.Dag, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

save(self: pybnesian.Dag, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

to_pdag(self: pybnesian.Dag) → pybnesian.PartiallyDirectedGraph

Gets the PartiallyDirectedGraph (PDAG) that represents the equivalence class of this Dag.

It implements the DAG-to-PDAG algorithm in [dag2pdag]. See also [dag2pdag_extra].

Returns:

A PartiallyDirectedGraph that represents the equivalence class of this Dag.

topological_sort(self: pybnesian.Dag) → list[str]

Gets the topological sort of the DAG.

Returns:

Topological sort as a list of nodes.

unconditional_graph(self: pybnesian.Dag) → pybnesian.Dag

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.PartiallyDirectedGraph

Partially directed graph. This graph can have edges and arcs.

static CompleteUndirected(nodes: list[str]) → pybnesian.PartiallyDirectedGraph

Creates a PartiallyDirectedGraph that is a complete undirected graph.

Parameters:

nodes – Nodes of the PartiallyDirectedGraph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.PartiallyDirectedGraph) -> None

Creates a PartiallyDirectedGraph without nodes, arcs and edges.

2. __init__(self: pybnesian.PartiallyDirectedGraph, nodes: list[str]) -> None

Creates a PartiallyDirectedGraph with the specified nodes and without arcs and edges.

Parameters:

nodes – Nodes of the PartiallyDirectedGraph.

3. __init__(self: pybnesian.PartiallyDirectedGraph, arcs: list[tuple[str, str]], edges: list[tuple[str, str]]) -> None

Creates a PartiallyDirectedGraph with the specified arcs and edges (the nodes are extracted from the arcs and edges).

Parameters:

• arcs – Arcs of the PartiallyDirectedGraph.

• edges – Edges of the PartiallyDirectedGraph.

4. __init__(self: pybnesian.PartiallyDirectedGraph, nodes: list[str], arcs: list[tuple[str, str]], edges: list[tuple[str, str]]) -> None

Creates a PartiallyDirectedGraph with the specified nodes and arcs.

Parameters:

• nodes – Nodes of the PartiallyDirectedGraph.

• arcs – Arcs of the PartiallyDirectedGraph.

• edges – Edges of the PartiallyDirectedGraph.

add_arc(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

add_edge(self: pybnesian.PartiallyDirectedGraph, n1: int or str, n2: int or str) → None

Adds an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

add_node(self: pybnesian.PartiallyDirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

arcs(self: pybnesian.PartiallyDirectedGraph) → list[tuple[str, str]]

Gets the list of arcs.

Returns:

A list of tuples (source, target) representing an arc source -> target.

children(self: pybnesian.PartiallyDirectedGraph, node: int or str) → List[str]

Gets the children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Children node names.

collapsed_from_index(self: pybnesian.PartiallyDirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.PartiallyDirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.PartiallyDirectedGraph) → dict[str, int]

Gets the collapsed indices in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.PartiallyDirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.PartiallyDirectedGraph) -> pybnesian.ConditionalPartiallyDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.PartiallyDirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalPartiallyDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_node(self: pybnesian.PartiallyDirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

direct(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → None

Transformation to create the arc source -> target when possible.

• If there is an edge source – target, it is transformed into an arc source -> target.

• If there is an arc target -> source, it is flipped into an arc source -> target.

• Else, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

edges(self: pybnesian.PartiallyDirectedGraph) → list[tuple[str, str]]

Gets the list of edges.

Returns:

A list of tuples (n1, n2) representing an edge between n1 and n2.

flip_arc(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

has_arc(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target exists.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc exists, False otherwise.

has_connection(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → bool

Checks whether two nodes source and target are connected.

Two nodes source and target are connected if there is an edge source – target, or an arc source -> target or an arc target -> source.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if source and target are connected, False otherwise.

has_edge(self: pybnesian.PartiallyDirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether an edge between the nodes n1 and n2 exists.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if the edge exists, False otherwise.

index(self: pybnesian.PartiallyDirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.PartiallyDirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.PartiallyDirectedGraph) → dict[str, int]

Gets all the indices in the graph.

Returns:

A dictionary with the index of each node.

is_leaf(self: pybnesian.PartiallyDirectedGraph, node: int or str) → bool

Checks whether node is a leaf node. A root node do not have children nodes.

Parameters:

node – A node name or index.

Returns:

True if node is leaf, False otherwise.

is_root(self: pybnesian.PartiallyDirectedGraph, node: int or str) → bool

Checks whether node is a root node. A root node do not have parent nodes.

Parameters:

node – A node name or index.

Returns:

True if node is root, False otherwise.

is_valid(self: pybnesian.PartiallyDirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

leaves(self: pybnesian.PartiallyDirectedGraph) → set[str]

Gets the leaf nodes of the graph. A leaf node do not have children nodes.

Returns:

The set of leaf nodes.

name(self: pybnesian.PartiallyDirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

neighbors(self: pybnesian.PartiallyDirectedGraph, node: int or str) → List[str]

Gets the neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Neighbor names.

nodes(self: pybnesian.PartiallyDirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_arcs(self: pybnesian.PartiallyDirectedGraph) → int

Gets the number of arcs.

Returns:

Number of arcs.

num_children(self: pybnesian.PartiallyDirectedGraph, node: int or str) → int

Gets the number of children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of children nodes.

num_edges(self: pybnesian.PartiallyDirectedGraph) → int

Gets the number of edges.

Returns:

Number of edges.

num_neighbors(self: pybnesian.PartiallyDirectedGraph, node: int or str) → int

Gets the number of neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Number of neighbors.

num_nodes(self: pybnesian.PartiallyDirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

num_parents(self: pybnesian.PartiallyDirectedGraph, node: int or str) → int

Gets the number of parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of parent nodes.

parents(self: pybnesian.PartiallyDirectedGraph, node: int or str) → List[str]

Gets the parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Parent node names.

remove_arc(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → None

Removes an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

remove_edge(self: pybnesian.PartiallyDirectedGraph, n1: int or str, n2: int or str) → None

Removes an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

remove_node(self: pybnesian.PartiallyDirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

roots(self: pybnesian.PartiallyDirectedGraph) → set[str]

Gets the root nodes of the graph. A root node do not have parent nodes.

Returns:

The set of root nodes.

save(self: pybnesian.PartiallyDirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

to_approximate_dag(self: pybnesian.PartiallyDirectedGraph) → pybnesian.Dag

Gets a Dag approximate extension of self. This method can be useful when PartiallyDirectedGraph.to_dag() cannot return a valid extension.

The algorithm is based on generating a topological sort which tries to preserve a similar structure.

Returns:

A Dag approximate extension of self.

to_dag(self: pybnesian.PartiallyDirectedGraph) → pybnesian.Dag

Gets a Dag which belongs to the equivalence class of self.

It implements the algorithm in [pdag2dag].

Returns:

A Dag which belongs to the equivalence class of self.

Raises:

ValueError – If self do not have a valid DAG extension.

unconditional_graph(self: pybnesian.PartiallyDirectedGraph) → pybnesian.PartiallyDirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

undirect(self: pybnesian.PartiallyDirectedGraph, source: int or str, target: int or str) → None

Transformation to create the edge source – target when possible.

• If there is not an arc target -> source, converts the arc source -> target into an edge source – target. If there is not an arc source -> target, it adds the edge source – target.

• Else, the graph is left unaffected

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Conditional Graphs

A conditional graph is the underlying graph in a conditional Bayesian networks ([PGM], Section 5.6). In a conditional Bayesian network, only the normal nodes can have a conditional probability density, while the interface nodes are always observed. A conditional graph splits all the nodes in two subsets: normal nodes and interface nodes. In a conditional graph, the interface nodes cannot have parents.

In a conditional graph, normal nodes can be returned with nodes(), the interface nodes with interface_nodes() and the joint set of nodes with joint_nodes(). Also, there are many other functions that have the prefix interface and joint to denote the interface and joint sets of nodes. Among them, there is a collapsed index version for only interface nodes, interface_collapsed_index(), and the joint set of nodes, joint_collapsed_index(). Note that the collapsed index for each set of nodes is independent.

class pybnesian.ConditionalUndirectedGraph

Conditional undirected graph.

static Complete(nodes: list[str], interface_nodes: list[str]) → pybnesian.ConditionalUndirectedGraph

Creates a complete ConditionalUndirectedGraph with the specified nodes. A complete conditional undirected graph connects every pair of nodes with an edge, except for pairs of interface nodes.

Parameters:

• nodes – Nodes of the ConditionalUndirectedGraph.

• interface_nodes – Interface nodes of the ConditionalUndirectedGraph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.ConditionalUndirectedGraph) -> None

Creates a ConditionalUndirectedGraph without nodes or edges.

2. __init__(self: pybnesian.ConditionalUndirectedGraph, nodes: list[str], interface_nodes: list[str]) -> None

Creates a ConditionalUndirectedGraph with the specified nodes, interface_nodes and without edges.

Parameters:

• nodes – Nodes of the ConditionalUndirectedGraph.

• interface_nodes – Interface nodes of the ConditionalUndirectedGraph.

3. __init__(self: pybnesian.ConditionalUndirectedGraph, nodes: list[str], interface_nodes: list[str], edges: list[tuple[str, str]]) -> None

Creates a ConditionalUndirectedGraph with the specified nodes, interface_nodes and edges.

Parameters:

• nodes – Nodes of the ConditionalUndirectedGraph.

• interface_nodes – Interface nodes of the ConditionalUndirectedGraph.

• edges – Edges of the ConditionalUndirectedGraph.

add_edge(self: pybnesian.ConditionalUndirectedGraph, n1: int or str, n2: int or str) → None

Adds an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

add_interface_node(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Adds an interface node to the graph and returns its index.

Parameters:

node – Name of the new interface node.

Returns:

Index of the new interface node.

add_node(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

collapsed_from_index(self: pybnesian.ConditionalUndirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.ConditionalUndirectedGraph) → dict[str, int]

Gets all the collapsed indices for the nodes in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.ConditionalUndirectedGraph) -> pybnesian.ConditionalUndirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.ConditionalUndirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalUndirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_interface_node(self: pybnesian.ConditionalUndirectedGraph, node: str) → bool

Tests whether the interface node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the interface node, False otherwise.

contains_joint_node(self: pybnesian.ConditionalUndirectedGraph, node: str) → bool

Tests whether the node is in the joint set of nodes or not.

Parameters:

node – Name of the node.

Returns:

True if the node is in the joint set of nodes, False otherwise.

contains_node(self: pybnesian.ConditionalUndirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

edges(self: pybnesian.ConditionalUndirectedGraph) → list[tuple[str, str]]

Gets the list of edges.

Returns:

A list of tuples (n1, n2) representing an edge between n1 and n2.

has_edge(self: pybnesian.ConditionalUndirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether an edge between the nodes n1 and n2 exists.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if the edge exists, False otherwise.

has_path(self: pybnesian.ConditionalUndirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether there is an undirected path between nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if there is an undirected path between n1 and n2, False otherwise.

index(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

index_from_interface_collapsed(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → int

Gets the index of a node from the interface collapsed index.

Parameters:

collapsed_index – Interface collapsed index of the node.

Returns:

Index of the node.

index_from_joint_collapsed(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → int

Gets the index of a node from the joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.ConditionalUndirectedGraph) → dict[str, int]

Gets all the indices for the nodes in the graph.

Returns:

A dictionary with the index of each node.

interface_collapsed_from_index(self: pybnesian.ConditionalUndirectedGraph, index: int) → int

Gets the interface collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Interface collapsed index of the node.

interface_collapsed_index(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Gets the interface collapsed index of an interface node from its name.

Parameters:

node – Name of the interface node.

Returns:

Interface collapsed index of the interface node.

interface_collapsed_indices(self: pybnesian.ConditionalUndirectedGraph) → dict[str, int]

Gets all the interface collapsed indices for the interface nodes in the graph.

Returns:

A dictionary with the interface collapsed index of each interface node.

interface_collapsed_name(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → str

Gets the name of an interface node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the interface node.

Returns:

Name of the interface node.

interface_edges(self: pybnesian.ConditionalUndirectedGraph) → list[tuple[str, str]]

Gets the edges where one of the nodes is an interface node.

Returns:

edges as a list of tuples (inode, node), where inode is an interface node and node is a normal node.

interface_nodes(self: pybnesian.ConditionalUndirectedGraph) → list[str]

Gets the interface nodes of the graph.

Returns:

Interface nodes of the graph.

is_interface(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → bool

Checks whether the node is an interface node.

Parameters:

node – A node name or index.

Returns:

True if node is interface node, False, otherwise.

is_valid(self: pybnesian.ConditionalUndirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

joint_collapsed_from_index(self: pybnesian.ConditionalUndirectedGraph, index: int) → int

Gets the joint collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_index(self: pybnesian.ConditionalUndirectedGraph, node: str) → int

Gets the joint collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_indices(self: pybnesian.ConditionalUndirectedGraph) → dict[str, int]

Gets all the joint collapsed indices for the joint set of nodes in the graph.

Returns:

A dictionary with the joint collapsed index of each joint node.

joint_collapsed_name(self: pybnesian.ConditionalUndirectedGraph, collapsed_index: int) → str

Gets the name of a node from its joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Name of the node.

joint_nodes(self: pybnesian.ConditionalUndirectedGraph) → list[str]

Gets the joint set of nodes of the graph.

Returns:

Joint set of nodes of the graph.

name(self: pybnesian.ConditionalUndirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

neighbors(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → List[str]

Gets the neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Neighbor names.

nodes(self: pybnesian.ConditionalUndirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_edges(self: pybnesian.ConditionalUndirectedGraph) → int

Gets the number of edges.

Returns:

Number of edges.

num_interface_nodes(self: pybnesian.ConditionalUndirectedGraph) → int

Gets the number of interface nodes.

Returns:

Number of interface nodes.

num_joint_nodes(self: pybnesian.ConditionalUndirectedGraph) → int

Gets the number of joint nodes. That is, num_nodes() + num_interface_nodes()

Returns:

Number of joint nodes.

num_neighbors(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → int

Gets the number of neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Number of neighbors.

num_nodes(self: pybnesian.ConditionalUndirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

remove_edge(self: pybnesian.ConditionalUndirectedGraph, n1: int or str, n2: int or str) → None

Removes an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

remove_interface_node(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → None

Removes an interface node.

Parameters:

node – A node name or index.

remove_node(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

save(self: pybnesian.ConditionalUndirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

set_interface(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → None

Converts a normal node into an interface node.

Parameters:

node – A node name or index.

set_node(self: pybnesian.ConditionalUndirectedGraph, node: int or str) → None

Converts an interface node into a normal node.

Parameters:

node – A node name or index.

unconditional_graph(self: pybnesian.ConditionalUndirectedGraph) → pybnesian.UndirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.ConditionalDirectedGraph

Conditional directed graph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.ConditionalDirectedGraph) -> None

Creates a ConditionalDirectedGraph without nodes or arcs.

2. __init__(self: pybnesian.ConditionalDirectedGraph, nodes: list[str], interface_nodes: list[str]) -> None

Creates a ConditionalDirectedGraph with the specified nodes, interface_nodes and without arcs.

Parameters:

• nodes – Nodes of the ConditionalDirectedGraph.

• interface_nodes – Interface nodes of the ConditionalDirectedGraph.

3. __init__(self: pybnesian.ConditionalDirectedGraph, nodes: list[str], interface_nodes: list[str], arcs: list[tuple[str, str]]) -> None

Creates a ConditionalDirectedGraph with the specified nodes and arcs.

Parameters:

• nodes – Nodes of the ConditionalDirectedGraph.

• interface_nodes – Interface nodes of the ConditionalDirectedGraph.

• arcs – Arcs of the ConditionalDirectedGraph.

add_arc(self: pybnesian.ConditionalDirectedGraph, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

add_interface_node(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Adds an interface node to the graph and returns its index.

Parameters:

node – Name of the new interface node.

Returns:

Index of the new interface node.

add_node(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

arcs(self: pybnesian.ConditionalDirectedGraph) → list[tuple[str, str]]

Gets the list of arcs.

Returns:

A list of tuples (source, target) representing an arc source -> target.

children(self: pybnesian.ConditionalDirectedGraph, node: int or str) → List[str]

Gets the children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Children node names.

collapsed_from_index(self: pybnesian.ConditionalDirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.ConditionalDirectedGraph) → dict[str, int]

Gets all the collapsed indices for the nodes in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.ConditionalDirectedGraph) -> pybnesian.ConditionalDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.ConditionalDirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_interface_node(self: pybnesian.ConditionalDirectedGraph, node: str) → bool

Tests whether the interface node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the interface node, False otherwise.

contains_joint_node(self: pybnesian.ConditionalDirectedGraph, node: str) → bool

Tests whether the node is in the joint set of nodes or not.

Parameters:

node – Name of the node.

Returns:

True if the node is in the joint set of nodes, False otherwise.

contains_node(self: pybnesian.ConditionalDirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

flip_arc(self: pybnesian.ConditionalDirectedGraph, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

has_arc(self: pybnesian.ConditionalDirectedGraph, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target exists.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc exists, False otherwise.

has_path(self: pybnesian.ConditionalDirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether there is a directed path between nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if there is an directed path between n1 and n2, False otherwise.

index(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

index_from_interface_collapsed(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → int

Gets the index of a node from the interface collapsed index.

Parameters:

collapsed_index – Interface collapsed index of the node.

Returns:

Index of the node.

index_from_joint_collapsed(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → int

Gets the index of a node from the joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.ConditionalDirectedGraph) → dict[str, int]

Gets all the indices for the nodes in the graph.

Returns:

A dictionary with the index of each node.

interface_arcs(self: pybnesian.ConditionalDirectedGraph) → list[tuple[str, str]]

Gets the arcs where the source node is an interface node.

Returns:

arcs with an interface node as source node.

interface_collapsed_from_index(self: pybnesian.ConditionalDirectedGraph, index: int) → int

Gets the interface collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Interface collapsed index of the node.

interface_collapsed_index(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Gets the interface collapsed index of an interface node from its name.

Parameters:

node – Name of the interface node.

Returns:

Interface collapsed index of the interface node.

interface_collapsed_indices(self: pybnesian.ConditionalDirectedGraph) → dict[str, int]

Gets all the interface collapsed indices for the interface nodes in the graph.

Returns:

A dictionary with the interface collapsed index of each interface node.

interface_collapsed_name(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → str

Gets the name of an interface node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the interface node.

Returns:

Name of the interface node.

interface_nodes(self: pybnesian.ConditionalDirectedGraph) → list[str]

Gets the interface nodes of the graph.

Returns:

Interface nodes of the graph.

is_interface(self: pybnesian.ConditionalDirectedGraph, node: int or str) → bool

Checks whether the node is an interface node.

Parameters:

node – A node name or index.

Returns:

True if node is interface node, False, otherwise.

is_leaf(self: pybnesian.ConditionalDirectedGraph, node: int or str) → bool

Checks whether node is a leaf node. A root node do not have children nodes.

Parameters:

node – A node name or index.

Returns:

True if node is leaf, False otherwise.

is_root(self: pybnesian.ConditionalDirectedGraph, node: int or str) → bool

Checks whether node is a root node. A root node do not have parent nodes.

This implementation do not take into account the interface arcs. That is, if a node only have interface nodes as parents, it is considered a root.

Parameters:

node – A node name or index.

Returns:

True if node is root, False otherwise.

is_valid(self: pybnesian.ConditionalDirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

joint_collapsed_from_index(self: pybnesian.ConditionalDirectedGraph, index: int) → int

Gets the joint collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_index(self: pybnesian.ConditionalDirectedGraph, node: str) → int

Gets the joint collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_indices(self: pybnesian.ConditionalDirectedGraph) → dict[str, int]

Gets all the joint collapsed indices for the joint set of nodes in the graph.

Returns:

A dictionary with the joint collapsed index of each joint node.

joint_collapsed_name(self: pybnesian.ConditionalDirectedGraph, collapsed_index: int) → str

Gets the name of a node from its joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Name of the node.

joint_nodes(self: pybnesian.ConditionalDirectedGraph) → list[str]

Gets the joint set of nodes of the graph.

Returns:

Joint set of nodes of the graph.

leaves(self: pybnesian.ConditionalDirectedGraph) → set[str]

Gets the leaf nodes of the graph. A leaf node do not have children nodes.

This implementation do not include the interface nodes in the result. Thus, this returns the same result as an unconditional graph without the interface nodes.

Returns:

The set of leaf nodes.

name(self: pybnesian.ConditionalDirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

nodes(self: pybnesian.ConditionalDirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_arcs(self: pybnesian.ConditionalDirectedGraph) → int

Gets the number of arcs.

Returns:

Number of arcs.

num_children(self: pybnesian.ConditionalDirectedGraph, node: int or str) → int

Gets the number of children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of children nodes.

num_interface_nodes(self: pybnesian.ConditionalDirectedGraph) → int

Gets the number of interface nodes.

Returns:

Number of interface nodes.

num_joint_nodes(self: pybnesian.ConditionalDirectedGraph) → int

Gets the number of joint nodes. That is, num_nodes() + num_interface_nodes()

Returns:

Number of joint nodes.

num_nodes(self: pybnesian.ConditionalDirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

num_parents(self: pybnesian.ConditionalDirectedGraph, node: int or str) → int

Gets the number of parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of parent nodes.

parents(self: pybnesian.ConditionalDirectedGraph, node: int or str) → List[str]

Gets the parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Parent node names.

remove_arc(self: pybnesian.ConditionalDirectedGraph, source: int or str, target: int or str) → None

Removes an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

remove_interface_node(self: pybnesian.ConditionalDirectedGraph, node: int or str) → None

Removes an interface node.

Parameters:

node – A node name or index.

remove_node(self: pybnesian.ConditionalDirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

roots(self: pybnesian.ConditionalDirectedGraph) → set[str]

Gets the root nodes of the graph. A root node do not have parent nodes.

This implementation do not include the interface nodes in the result. Also, do not take into account the interface arcs. That is, if a node only have interface nodes as parents, it is considered a root. Thus, this returns the same result as an unconditional graph without the interface nodes.

Returns:

The set of root nodes.

save(self: pybnesian.ConditionalDirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

set_interface(self: pybnesian.ConditionalDirectedGraph, node: int or str) → None

Converts a normal node into an interface node.

Parameters:

node – A node name or index.

set_node(self: pybnesian.ConditionalDirectedGraph, node: int or str) → None

Converts an interface node into a normal node.

Parameters:

node – A node name or index.

unconditional_graph(self: pybnesian.ConditionalDirectedGraph) → pybnesian.DirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.ConditionalDag

Bases: ConditionalDirectedGraph

Conditional directed acyclic graph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.ConditionalDag) -> None

Creates a ConditionalDag without nodes or arcs.

2. __init__(self: pybnesian.ConditionalDag, nodes: list[str], interface_nodes: list[str]) -> None

Creates a ConditionalDag with the specified nodes, interface_nodes and without arcs.

Parameters:

• nodes – Nodes of the ConditionalDag.

• interface_nodes – Interface nodes of the ConditionalDag.

3. __init__(self: pybnesian.ConditionalDag, nodes: list[str], interface_nodes: list[str], arcs: list[tuple[str, str]]) -> None

Creates a ConditionalDag with the specified nodes, interface_nodes and arcs.

Parameters:

• nodes – Nodes of the ConditionalDag.

• interface_nodes – Interface nod”es of the ConditionalDag.

• arcs – Arcs of the ConditionalDag.

add_arc(self: pybnesian.ConditionalDag, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

can_add_arc(self: pybnesian.ConditionalDag, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target can be added. That is, the arc is valid and do not generate a cycle or connects two interface nodes.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc can be added, False otherwise.

can_flip_arc(self: pybnesian.ConditionalDag, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target can be flipped. That is, the flipped arc is valid and do not generate a cycle. If the arc source -> target do not exist, it will return ConditionalDag.can_add_arc().

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc can be flipped, False otherwise.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.ConditionalDag) -> pybnesian.ConditionalDag

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.ConditionalDag, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalDag

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

flip_arc(self: pybnesian.ConditionalDag, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

save(self: pybnesian.ConditionalDag, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

to_pdag(self: pybnesian.ConditionalDag) → pybnesian.ConditionalPartiallyDirectedGraph

Gets the ConditionalPartiallyDirectedGraph (PDAG) that represents the equivalence class of this ConditionalDag.

It implements the DAG-to-PDAG algorithm in [dag2pdag]. See also [dag2pdag_extra].

Returns:

A ConditionalPartiallyDirectedGraph that represents the equivalence class of this ConditionalDag.

topological_sort(self: pybnesian.ConditionalDag) → list[str]

Gets the topological sort of the conditional DAG. This topological sort does not include the interface nodes, since they are known to be always roots (they can be included at the very beginning of the topological sort).

Returns:

Topological sort as a list of nodes.

unconditional_graph(self: pybnesian.ConditionalDag) → pybnesian.Dag

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

class pybnesian.ConditionalPartiallyDirectedGraph

Conditional partially directed graph. This graph can have edges and arcs, except between pairs of interface nodes.

static CompleteUndirected(nodes: list[str], interface_nodes: list[str]) → pybnesian.ConditionalPartiallyDirectedGraph

Creates a ConditionalPartiallyDirectedGraph that is a complete undirected graph. A complete conditional undirected graph connects every pair of nodes with an edge, except for pairs of interface nodes.

Parameters:

• nodes – Nodes of the ConditionalPartiallyDirectedGraph.

• interface_nodes – Interface nodes of the ConditionalPartiallyDirectedGraph.

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pybnesian.ConditionalPartiallyDirectedGraph) -> None

Creates a ConditionalPartiallyDirectedGraph without nodes or arcs.

2. __init__(self: pybnesian.ConditionalPartiallyDirectedGraph, nodes: list[str], interface_nodes: list[str]) -> None

Creates a ConditionalPartiallyDirectedGraph with the specified nodes, interface_nodes and without edges.

Parameters:

• nodes – Nodes of the ConditionalPartiallyDirectedGraph.

• interface_nodes – Interface nodes of the ConditionalPartiallyDirectedGraph.

3. __init__(self: pybnesian.ConditionalPartiallyDirectedGraph, nodes: list[str], interface_nodes: list[str], arcs: list[tuple[str, str]], edges: list[tuple[str, str]]) -> None

Creates a ConditionalPartiallyDirectedGraph with the specified nodes and arcs.

Parameters:

• nodes – Nodes of the ConditionalPartiallyDirectedGraph.

• interface_nodes – Interface nodes of the ConditionalPartiallyDirectedGraph.

• arcs – Arcs of the ConditionalPartiallyDirectedGraph.

• edges – Edges of the ConditionalPartiallyDirectedGraph.

add_arc(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → None

Adds an arc between the nodes source and target. If the arc already exists, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

add_edge(self: pybnesian.ConditionalPartiallyDirectedGraph, n1: int or str, n2: int or str) → None

Adds an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

add_interface_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Adds an interface node to the graph and returns its index.

Parameters:

node – Name of the new interface node.

Returns:

Index of the new interface node.

add_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Adds a node to the graph and returns its index.

Parameters:

node – Name of the new node.

Returns:

Index of the new node.

arcs(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[tuple[str, str]]

Gets the list of arcs.

Returns:

A list of tuples (source, target) representing an arc source -> target.

children(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → List[str]

Gets the children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Children node names.

collapsed_from_index(self: pybnesian.ConditionalPartiallyDirectedGraph, index: int) → int

Gets the collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Collapsed index of the node.

collapsed_index(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Gets the collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Collapsed index of the node.

collapsed_indices(self: pybnesian.ConditionalPartiallyDirectedGraph) → dict[str, int]

Gets all the collapsed indices for the nodes in the graph.

Returns:

A dictionary with the collapsed index of each node.

collapsed_name(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → str

Gets the name of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Name of the node.

conditional_graph(*args, **kwargs)

Overloaded function.

1. conditional_graph(self: pybnesian.ConditionalPartiallyDirectedGraph) -> pybnesian.ConditionalPartiallyDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the same nodes and without interface nodes.

• If self is conditional, it returns a copy of self.

Returns:

The conditional graph transformation of self.

2. conditional_graph(self: pybnesian.ConditionalPartiallyDirectedGraph, nodes: list[str], interface_nodes: list[str]) -> pybnesian.ConditionalPartiallyDirectedGraph

Transforms the graph to a conditional graph.

• If self is not conditional, it returns a conditional version of the graph with the given nodes and interface nodes.

• If self is conditional, it returns the same graph type with the given nodes and interface nodes.

Parameters:

• nodes – The nodes for the new conditional graph.

• interface_nodes – The interface nodes for the new conditional graph.

Returns:

The conditional graph transformation of self.

contains_interface_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → bool

Tests whether the interface node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the interface node, False otherwise.

contains_joint_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → bool

Tests whether the node is in the joint set of nodes or not.

Parameters:

node – Name of the node.

Returns:

True if the node is in the joint set of nodes, False otherwise.

contains_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → bool

Tests whether the node is in the graph or not.

Parameters:

node – Name of the node.

Returns:

True if the graph contains the node, False otherwise.

direct(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → None

Transformation to create the arc source -> target when possible.

• If there is an edge source – target, it is transformed into an arc source -> target.

• If there is an arc target -> source, it is flipped into an arc source -> target.

• Else, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

edges(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[tuple[str, str]]

Gets the list of edges.

Returns:

A list of tuples (n1, n2) representing an edge between n1 and n2.

flip_arc(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → None

Flips (reverses) an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

has_arc(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → bool

Checks whether an arc between the nodes source and target exists.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if the arc exists, False otherwise.

has_connection(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → bool

Checks whether two nodes source and target are connected.

Two nodes source and target are connected if there is an edge source – target, or an arc source -> target or an arc target -> source.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Returns:

True if source and target are connected, False otherwise.

has_edge(self: pybnesian.ConditionalPartiallyDirectedGraph, n1: int or str, n2: int or str) → bool

Checks whether an edge between the nodes n1 and n2 exists.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

Returns:

True if the edge exists, False otherwise.

index(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Gets the index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Index of the node.

index_from_collapsed(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → int

Gets the index of a node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the node.

Returns:

Index of the node.

index_from_interface_collapsed(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → int

Gets the index of a node from the interface collapsed index.

Parameters:

collapsed_index – Interface collapsed index of the node.

Returns:

Index of the node.

index_from_joint_collapsed(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → int

Gets the index of a node from the joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Index of the node.

indices(self: pybnesian.ConditionalPartiallyDirectedGraph) → dict[str, int]

Gets all the indices for the nodes in the graph.

Returns:

A dictionary with the index of each node.

interface_arcs(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[tuple[str, str]]

Gets the arcs where the source node is an interface node.

Returns:

arcs with an interface node as source node.

interface_collapsed_from_index(self: pybnesian.ConditionalPartiallyDirectedGraph, index: int) → int

Gets the interface collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Interface collapsed index of the node.

interface_collapsed_index(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Gets the interface collapsed index of an interface node from its name.

Parameters:

node – Name of the interface node.

Returns:

Interface collapsed index of the interface node.

interface_collapsed_indices(self: pybnesian.ConditionalPartiallyDirectedGraph) → dict[str, int]

Gets all the interface collapsed indices for the interface nodes in the graph.

Returns:

A dictionary with the interface collapsed index of each interface node.

interface_collapsed_name(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → str

Gets the name of an interface node from its collapsed index.

Parameters:

collapsed_index – Collapsed index of the interface node.

Returns:

Name of the interface node.

interface_edges(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[tuple[str, str]]

Gets the edges where one of the nodes is an interface node.

Returns:

edges as a list of tuples (inode, node), where inode is an interface node and node is a normal node.

interface_nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[str]

Gets the interface nodes of the graph.

Returns:

Interface nodes of the graph.

is_interface(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → bool

Checks whether the node is an interface node.

Parameters:

node – A node name or index.

Returns:

True if node is interface node, False, otherwise.

is_leaf(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → bool

Checks whether node is a leaf node. A root node do not have children nodes.

Parameters:

node – A node name or index.

Returns:

True if node is leaf, False otherwise.

is_root(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → bool

Checks whether node is a root node. A root node do not have parent nodes.

This implementation do not take into account the interface arcs. That is, if a node only have interface nodes as parents, it is considered a root.

Parameters:

node – A node name or index.

Returns:

True if node is root, False otherwise.

is_valid(self: pybnesian.ConditionalPartiallyDirectedGraph, index: int) → bool

Checks whether a index is a valid index (the node is not removed). All the valid indices are always returned by indices().

Parameters:

index – Index of the node.

Returns:

True if the index is valid, False otherwise.

joint_collapsed_from_index(self: pybnesian.ConditionalPartiallyDirectedGraph, index: int) → int

Gets the joint collapsed index of a node from its index.

Parameters:

index – Index of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_index(self: pybnesian.ConditionalPartiallyDirectedGraph, node: str) → int

Gets the joint collapsed index of a node from its name.

Parameters:

node – Name of the node.

Returns:

Joint collapsed index of the node.

joint_collapsed_indices(self: pybnesian.ConditionalPartiallyDirectedGraph) → dict[str, int]

Gets all the joint collapsed indices for the joint set of nodes in the graph.

Returns:

A dictionary with the joint collapsed index of each joint node.

joint_collapsed_name(self: pybnesian.ConditionalPartiallyDirectedGraph, collapsed_index: int) → str

Gets the name of a node from its joint collapsed index.

Parameters:

collapsed_index – Joint collapsed index of the node.

Returns:

Name of the node.

joint_nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[str]

Gets the joint set of nodes of the graph.

Returns:

Joint set of nodes of the graph.

leaves(self: pybnesian.ConditionalPartiallyDirectedGraph) → set[str]

Gets the leaf nodes of the graph. A leaf node do not have children nodes.

This implementation do not include the interface nodes in the result. Thus, this returns the same result as an unconditional graph without the interface nodes.

Returns:

The set of leaf nodes.

name(self: pybnesian.ConditionalPartiallyDirectedGraph, index: int) → str

Gets the name of a node from its index.

Parameters:

index – Index of the node.

Returns:

Name of the node.

neighbors(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → List[str]

Gets the neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Neighbor names.

nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → list[str]

Gets the nodes of the graph.

Returns:

Nodes of the graph.

num_arcs(self: pybnesian.ConditionalPartiallyDirectedGraph) → int

Gets the number of arcs.

Returns:

Number of arcs.

num_children(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → int

Gets the number of children nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of children nodes.

num_edges(self: pybnesian.ConditionalPartiallyDirectedGraph) → int

Gets the number of edges.

Returns:

Number of edges.

num_interface_nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → int

Gets the number of interface nodes.

Returns:

Number of interface nodes.

num_joint_nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → int

Gets the number of joint nodes. That is, num_nodes() + num_interface_nodes()

Returns:

Number of joint nodes.

num_neighbors(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → int

Gets the number of neighbors (adjacent nodes by an edge) of a node.

Parameters:

node – A node name or index.

Returns:

Number of neighbors.

num_nodes(self: pybnesian.ConditionalPartiallyDirectedGraph) → int

Gets the number of nodes.

Returns:

Number of nodes.

num_parents(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → int

Gets the number of parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Number of parent nodes.

parents(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → List[str]

Gets the parent nodes of a node.

Parameters:

node – A node name or index.

Returns:

Parent node names.

remove_arc(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → None

Removes an arc between the nodes source and target. If the arc do not exist, the graph is left unaffected.

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

remove_edge(self: pybnesian.ConditionalPartiallyDirectedGraph, n1: int or str, n2: int or str) → None

Removes an edge between the nodes n1 and n2.

n1 and n2 can be the name or the index, but the type of n1 and n2 must be the same.

Parameters:

• n1 – A node name or index.

• n2 – A node name or index.

remove_interface_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → None

Removes an interface node.

Parameters:

node – A node name or index.

remove_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → None

Removes a node.

Parameters:

node – A node name or index.

roots(self: pybnesian.ConditionalPartiallyDirectedGraph) → set[str]

Gets the root nodes of the graph. A root node do not have parent nodes.

This implementation do not include the interface nodes in the result. Also, do not take into account the interface arcs. That is, if a node only have interface nodes as parents, it is considered a root. Thus, this returns the same result as an unconditional graph without the interface nodes.

Returns:

The set of root nodes.

save(self: pybnesian.ConditionalPartiallyDirectedGraph, filename: str) → None

Saves the graph in a pickle file with the given name.

Parameters:

filename – File name of the saved graph.

set_interface(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → None

Converts a normal node into an interface node.

Parameters:

node – A node name or index.

set_node(self: pybnesian.ConditionalPartiallyDirectedGraph, node: int or str) → None

Converts an interface node into a normal node.

Parameters:

node – A node name or index.

to_approximate_dag(self: pybnesian.ConditionalPartiallyDirectedGraph) → pybnesian.ConditionalDag

Gets a Dag approximate extension of self. This method can be useful when ConditionalPartiallyDirectedGraph.to_dag() cannot return a valid extension.

The algorithm is based on generating a topological sort which tries to preserve a similar structure.

Returns:

A Dag approximate extension of self.

to_dag(self: pybnesian.ConditionalPartiallyDirectedGraph) → pybnesian.ConditionalDag

Gets a Dag which belongs to the equivalence class of self.

It implements the algorithm in [pdag2dag].

Returns:

A Dag which belongs to the equivalence class of self.

Raises:

ValueError – If self do not have a valid DAG extension.

unconditional_graph(self: pybnesian.ConditionalPartiallyDirectedGraph) → pybnesian.PartiallyDirectedGraph

Transforms the graph to an unconditional graph.

• If self is not conditional, it returns a copy of self.

• If self is conditional, the interface nodes are included as nodes in the returned graph.

Returns:

The unconditional graph transformation of self.

undirect(self: pybnesian.ConditionalPartiallyDirectedGraph, source: int or str, target: int or str) → None

Transformation to create the edge source – target when possible.

• If there is not an arc target -> source, converts the arc source -> target into an edge source – target. If there is not an arc source -> target, it adds the edge source – target.

• Else, the graph is left unaffected

source and target can be the name or the index, but the type of source and target must be the same.

Parameters:

• source – A node name or index.

• target – A node name or index.

Bibliography

[dag2pdag] (1,2)

Chickering, M. (2002). Learning Equivalence Classes of Bayesian-Network Structures. Journal of Machine Learning Research, 2, 445-498.

[dag2pdag_extra] (1,2)

Chickering, M. (1995). A Transformational Characterization of Equivalent Bayesian Network Structures. Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI’95), Montreal.

[pdag2dag] (1,2)

Dorit, D. and Tarsi, M. (1992). A simple algorithm to construct a consistent extension of a partially oriented graph (Report No: R-185).

[PGM]

Koller, D. and Friedman, N. (2009). Probabilistic Graphical Models. MIT press.