Graph Algorithms#

Note

These functions are mostly geared towards directed graphs (digraphs).

pytools.graph.reverse_graph(graph: GraphT[NodeT]) → GraphT[NodeT][source]#

Reverses a graph graph.

pytools.graph.a_star(initial_state: NodeT, goal_state: NodeT, neighbor_map: GraphT[NodeT], estimate_remaining_cost: Optional[Callable[[NodeT], float]] = None, get_step_cost: Callable[[Any, NodeT], float] = <function <lambda>>) → List[NodeT][source]#: With the default cost and heuristic, this amounts to Dijkstra’s algorithm.

pytools.graph.compute_sccs(graph: GraphT[NodeT]) → List[List[NodeT]][source]#

exception pytools.graph.CycleError(node: pytools.graph.NodeT)[source]#

Raised when a topological ordering cannot be computed due to a cycle.

pytools.graph.compute_topological_order(graph: GraphT[NodeT], key: Callable[[NodeT], Any] | None = None) → List[NodeT][source]#

Compute a topological order of nodes in a directed graph.

Parameters:: key – A custom key function may be supplied to determine the order in break-even cases. Expects a function of one argument that is used to extract a comparison key from each node of the graph.
Returns:: A list representing a valid topological ordering of the nodes in the directed graph.

Note

New in version 2020.2.

pytools.graph.compute_transitive_closure(graph: Mapping[NodeT, MutableSet[NodeT]]) → GraphT[NodeT][source]#

Compute the transitive closure of a directed graph using Warshall’s algorithm.

Parameters:: graph – A collections.abc.Mapping representing a directed graph. The mapping contains one key representing each node in the graph, and this key maps to a collections.abc.MutableSet of nodes that are connected to the node by outgoing edges. This graph may contain cycles. This object must be picklable. Every graph node must be included as a key in the graph.
Returns:: The transitive closure of the graph, represented using the same data type.

New in version 2020.2.

pytools.graph.contains_cycle(graph: GraphT[NodeT]) → bool[source]#

Determine whether a graph contains a cycle.

New in version 2020.2.

pytools.graph.compute_induced_subgraph(graph: Mapping[NodeT, Set[NodeT]], subgraph_nodes: Set[NodeT]) → GraphT[NodeT][source]#

Compute the induced subgraph formed by a subset of the vertices in a graph.

Parameters:

graph – A collections.abc.Mapping representing a directed graph. The mapping contains one key representing each node in the graph, and this key maps to a collections.abc.Set of nodes that are connected to the node by outgoing edges.
subgraph_nodes – A collections.abc.Set containing a subset of the graph nodes in the graph.

Returns:

A dict representing the induced subgraph formed by the subset of the vertices included in subgraph_nodes.

New in version 2020.2.

pytools.graph.as_graphviz_dot(graph: GraphT[NodeT], node_labels: Callable[[NodeT], str] | None = None, edge_labels: Callable[[NodeT, NodeT], str] | None = None) → str[source]#

Create a visualization of the graph graph in the dot language.

Parameters:

node_labels – An optional function that returns node labels for each node.
edge_labels – An optional function that returns edge labels for each pair of nodes.

Returns:

A string in the dot language.

pytools.graph.validate_graph(graph: GraphT[NodeT]) → None[source]#: Validates that all successor nodes of each node in graph are keys in graph itself. Raises a ValueError if not.

pytools.graph.is_connected(graph: GraphT[NodeT]) → bool[source]#

Returns whether all nodes in graph are connected, ignoring the edge direction.

Type Variables Used#

class pytools.graph.NodeT#: Type of a graph node, can be any hashable type.

class pytools.graph.GraphT#: A collections.abc.Mapping representing a directed graph. The mapping contains one key representing each node in the graph, and this key maps to a collections.abc.Collection of its successor nodes. Note that most functions expect that every graph node is included as a key in the graph.