# This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory # of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. # # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. import sys import functools from .rustworkx import * # flake8: noqa import rustworkx.visit sys.modules["rustworkx.generators"] = generators class PyDAG(PyDiGraph): """A class for creating direct acyclic graphs. PyDAG is just an alias of the PyDiGraph class and behaves identically to the :class:`~rustworkx.PyDiGraph` class and can be used interchangably with ``PyDiGraph``. It currently exists solely as a backwards compatibility alias for users of rustworkx from prior to the 0.4.0 release when there was no PyDiGraph class. The PyDAG class is used to create a directed graph. It can be a multigraph (have multiple edges between nodes). Each node and edge (although rarely used for edges) is indexed by an integer id. These ids are stable for the lifetime of the graph object and on node or edge deletions you can have holes in the list of indices for the graph. Node indices will be reused on additions after removal. For example: .. jupyter-execute:: import rustworkx as rx graph = rx.PyDAG() graph.add_nodes_from(list(range(5))) graph.add_nodes_from(list(range(2))) graph.remove_node(2) print("After deletion:", graph.node_indices()) res_manual = graph.add_parent(6, None, None) print("After adding a new node:", graph.node_indices()) Additionally, each node and edge contains an arbitrary Python object as a weight/data payload. You can use the index for access to the data payload as in the following example: .. jupyter-execute:: import rustworkx as rx graph = rx.PyDAG() data_payload = "An arbitrary Python object" node_index = graph.add_node(data_payload) print("Node Index: %s" % node_index) print(graph[node_index]) The PyDAG class implements the Python mapping protocol for nodes so in addition to access you can also update the data payload with: .. jupyter-execute:: import rustworkx as rx graph = rx.PyDAG() data_payload = "An arbitrary Python object" node_index = graph.add_node(data_payload) graph[node_index] = "New Payload" print("Node Index: %s" % node_index) print(graph[node_index]) The PyDAG class has an option for real time cycle checking which can be used to ensure any edges added to the graph does not introduce a cycle. By default the real time cycle checking feature is disabled for performance, however you can enable it by setting the ``check_cycle`` attribute to True. For example:: import rustworkx as rx dag = rx.PyDAG() dag.check_cycle = True or at object creation:: import rustworkx as rx dag = rx.PyDAG(check_cycle=True) With check_cycle set to true any calls to :meth:`PyDAG.add_edge` will ensure that no cycles are added, ensuring that the PyDAG class truly represents a directed acyclic graph. Do note that this cycle checking on :meth:`~PyDAG.add_edge`, :meth:`~PyDigraph.add_edges_from`, :meth:`~PyDAG.add_edges_from_no_data`, :meth:`~PyDAG.extend_from_edge_list`, and :meth:`~PyDAG.extend_from_weighted_edge_list` comes with a performance penalty that grows as the graph does. If you're adding a node and edge at the same time, leveraging :meth:`PyDAG.add_child` or :meth:`PyDAG.add_parent` will avoid this overhead. By default a ``PyDAG`` is a multigraph (meaning there can be parallel edges between nodes) however this can be disabled by setting the ``multigraph`` kwarg to ``False`` when calling the ``PyDAG`` constructor. For example:: import rustworkx as rx dag = rx.PyDAG(multigraph=False) This can only be set at ``PyDiGraph`` initialization and not adjusted after creation. When :attr:`~rustworkx.PyDiGraph.multigraph` is set to ``False`` if a method call is made that would add a parallel edge it will instead update the existing edge's weight/data payload. The maximum number of nodes and edges allowed on a ``PyGraph`` object is :math:`2^{32} - 1` (4,294,967,294) each. Attempting to add more nodes or edges than this will result in an exception being raised. :param bool check_cycle: When this is set to ``True`` the created ``PyDAG`` has runtime cycle detection enabled. :param bool multgraph: When this is set to ``False`` the created ``PyDAG`` object will not be a multigraph. When ``False`` if a method call is made that would add parallel edges the the weight/weight from that method call will be used to update the existing edge in place. """ pass @functools.singledispatch def distance_matrix(graph, parallel_threshold=300, as_undirected=False, null_value=0.0): """Get the distance matrix for a graph This differs from functions like :func:`~rustworkx.floyd_warshall_numpy` in that the edge weight/data payload is not used and each edge is treated as a distance of 1. This function is also multithreaded and will run in parallel if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 300). If the function will be running in parallel the env var ``RAYON_NUM_THREADS`` can be used to adjust how many threads will be used. :param graph: The graph to get the distance matrix for, can be either a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param int parallel_threshold: The number of nodes to calculate the the distance matrix in parallel at. It defaults to 300, but this can be tuned :param bool as_undirected: If set to ``True`` the input directed graph will be treat as if each edge was bidirectional/undirected in the output distance matrix. :param float null_value: An optional float that will treated as a null value. This is the default value in the output matrix and it is used to indicate the absence of an edge between 2 nodes. By default this is ``0.0``. :returns: The distance matrix :rtype: numpy.ndarray """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) distance_matrix.register(PyDiGraph, digraph_distance_matrix) distance_matrix.register(PyGraph, graph_distance_matrix) @functools.singledispatch def unweighted_average_shortest_path_length(graph, parallel_threshold=300, disconnected=False): r"""Return the average shortest path length with unweighted edges. The average shortest path length is calculated as .. math:: a =\sum_{s,t \in V, s \ne t} \frac{d(s, t)}{n(n-1)} where :math:`V` is the set of nodes in ``graph``, :math:`d(s, t)` is the shortest path length from :math:`s` to :math:`t`, and :math:`n` is the number of nodes in ``graph``. If ``disconnected`` is set to ``True``, the average will be taken only between connected nodes. This function is also multithreaded and will run in parallel if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 300). If the function will be running in parallel the env var ``RAYON_NUM_THREADS`` can be used to adjust how many threads will be used. By default it will use all available CPUs if the environment variable is not specified. :param graph: The graph to compute the average shortest path length for, can be either a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param int parallel_threshold: The number of nodes to calculate the the distance matrix in parallel at. It defaults to 300, but this can be tuned to any number of nodes. :param bool as_undirected: If set to ``True`` the input directed graph will be treated as if each edge was bidirectional/undirected while finding the shortest paths. Default: ``False``. :param bool disconnected: If set to ``True`` only connected vertex pairs will be included in the calculation. If ``False``, infinity is returned for disconnected graphs. Default: ``False``. :returns: The average shortest path length. If no vertex pairs can be included in the calculation this will return NaN. :rtype: float """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) unweighted_average_shortest_path_length.register( PyDiGraph, digraph_unweighted_average_shortest_path_length ) unweighted_average_shortest_path_length.register( PyGraph, graph_unweighted_average_shortest_path_length ) @functools.singledispatch def adjacency_matrix(graph, weight_fn=None, default_weight=1.0, null_value=0.0): """Return the adjacency matrix for a graph object In the case where there are multiple edges between nodes the value in the output matrix will be the sum of the edges' weights. :param graph: The graph used to generate the adjacency matrix from. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param callable weight_fn: A callable object (function, lambda, etc) which will be passed the edge object and expected to return a ``float``. This tells rustworkx/rust how to extract a numerical weight as a ``float`` for edge object. Some simple examples are:: adjacency_matrix(graph, weight_fn: lambda x: 1) to return a weight of 1 for all edges. Also:: adjacency_matrix(graph, weight_fn: lambda x: float(x)) to cast the edge object as a float as the weight. If this is not specified a default value (either ``default_weight`` or 1) will be used for all edges. :param float default_weight: If ``weight_fn`` is not used this can be optionally used to specify a default weight to use for all edges. :param float null_value: An optional float that will treated as a null value. This is the default value in the output matrix and it is used to indicate the absence of an edge between 2 nodes. By default this is ``0.0``. :return: The adjacency matrix for the input dag as a numpy array :rtype: numpy.ndarray """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) adjacency_matrix.register(PyDiGraph, digraph_adjacency_matrix) adjacency_matrix.register(PyGraph, graph_adjacency_matrix) @functools.singledispatch def all_simple_paths(graph, from_, to, min_depth=None, cutoff=None): """Return all simple paths between 2 nodes in a PyGraph object A simple path is a path with no repeated nodes. :param graph: The graph to find the path in. Can either be a class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int from_: The node index to find the paths from :param int to: The node index to find the paths to :param int min_depth: The minimum depth of the path to include in the output list of paths. By default all paths are included regardless of depth, setting to 0 will behave like the default. :param int cutoff: The maximum depth of path to include in the output list of paths. By default includes all paths regardless of depth, setting to 0 will behave like default. :returns: A list of lists where each inner list is a path of node indices :rtype: list """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_simple_paths.register(PyDiGraph, digraph_all_simple_paths) all_simple_paths.register(PyGraph, graph_all_simple_paths) @functools.singledispatch def floyd_warshall( graph, weight_fn=None, default_weight=1.0, parallel_threshold=300, ): """Find all-pairs shortest path lengths using Floyd's algorithm Floyd's algorithm is used for finding shortest paths in dense graphs or graphs with negative weights (where Dijkstra's algorithm fails). This function is multithreaded and will launch a pool with threads equal to the number of CPUs by default if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 300). You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads if parallelization was enabled. :param graph: The graph to run Floyd's algorithm on. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param callable weight_fn: A callable object (function, lambda, etc) which will be passed the edge object and expected to return a ``float``. This tells rustworkx/rust how to extract a numerical weight as a ``float`` for edge object. Some simple examples are:: floyd_warshall(graph, weight_fn= lambda x: 1) to return a weight of 1 for all edges. Also:: floyd_warshall(graph, weight_fn=float) to cast the edge object as a float as the weight. If this is not specified a default value (either ``default_weight`` or 1) will be used for all edges. :param float default_weight: If ``weight_fn`` is not used this can be optionally used to specify a default weight to use for all edges. :param int parallel_threshold: The number of nodes to execute the algorithm in parallel at. It defaults to 300, but this can be tuned :return: A read-only dictionary of path lengths. The keys are the source node indices and the values are a dict of the target node and the length of the shortest path to that node. For example:: { 0: {0: 0.0, 1: 2.0, 2: 2.0}, 1: {1: 0.0, 2: 1.0}, 2: {0: 1.0, 2: 0.0}, } :rtype: AllPairsPathLengthMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) floyd_warshall.register(PyDiGraph, digraph_floyd_warshall) floyd_warshall.register(PyGraph, graph_floyd_warshall) @functools.singledispatch def floyd_warshall_numpy( graph, weight_fn=None, default_weight=1.0, parallel_threshold=300, ): """Find all-pairs shortest path lengths using Floyd's algorithm Floyd's algorithm is used for finding shortest paths in dense graphs or graphs with negative weights (where Dijkstra's algorithm fails). This function is multithreaded and will launch a pool with threads equal to the number of CPUs by default if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 300). You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads if parallelization was enabled. :param graph: The graph to run Floyd's algorithm on. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param callable weight_fn: A callable object (function, lambda, etc) which will be passed the edge object and expected to return a ``float``. This tells rustworkx/rust how to extract a numerical weight as a ``float`` for edge object. Some simple examples are:: floyd_warshall_numpy(graph, weight_fn: lambda x: 1) to return a weight of 1 for all edges. Also:: floyd_warshall_numpy(graph, weight_fn: lambda x: float(x)) to cast the edge object as a float as the weight. If this is not specified a default value (either ``default_weight`` or 1) will be used for all edges. :param float default_weight: If ``weight_fn`` is not used this can be optionally used to specify a default weight to use for all edges. :param int parallel_threshold: The number of nodes to execute the algorithm in parallel at. It defaults to 300, but this can be tuned :returns: A matrix of shortest path distances between nodes. If there is no path between two nodes then the corresponding matrix entry will be ``np.inf``. :rtype: numpy.ndarray """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) floyd_warshall_numpy.register(PyDiGraph, digraph_floyd_warshall_numpy) floyd_warshall_numpy.register(PyGraph, graph_floyd_warshall_numpy) @functools.singledispatch def astar_shortest_path(graph, node, goal_fn, edge_cost_fn, estimate_cost_fn): """Compute the A* shortest path for a graph :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int node: The node index to compute the path from :param goal_fn: A python callable that will take in 1 parameter, a node's data object and will return a boolean which will be True if it is the finish node. :param edge_cost_fn: A python callable that will take in 1 parameter, an edge's data object and will return a float that represents the cost of that edge. It must be non-negative. :param estimate_cost_fn: A python callable that will take in 1 parameter, a node's data object and will return a float which represents the estimated cost for the next node. The return must be non-negative. For the algorithm to find the actual shortest path, it should be admissible, meaning that it should never overestimate the actual cost to get to the nearest goal node. :returns: The computed shortest path between node and finish as a list of node indices. :rtype: NodeIndices """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) astar_shortest_path.register(PyDiGraph, digraph_astar_shortest_path) astar_shortest_path.register(PyGraph, graph_astar_shortest_path) @functools.singledispatch def dijkstra_shortest_paths( graph, source, target=None, weight_fn=None, default_weight=1.0, as_undirected=False, ): """Find the shortest path from a node This function will generate the shortest path from a source node using Dijkstra's algorithm. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int source: The node index to find paths from :param int target: An optional target to find a path to :param weight_fn: An optional weight function for an edge. It will accept a single argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :param float default_weight: If ``weight_fn`` isn't specified this optional float value will be used for the weight/cost of each edge. :param bool as_undirected: If set to true the graph will be treated as undirected for finding the shortest path. This only works with a :class:`~rustworkx.PyDiGraph` input for ``graph`` :return: Dictionary of paths. The keys are destination node indices and the dict values are lists of node indices making the path. :rtype: dict """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) dijkstra_shortest_paths.register(PyDiGraph, digraph_dijkstra_shortest_paths) dijkstra_shortest_paths.register(PyGraph, graph_dijkstra_shortest_paths) @functools.singledispatch def has_path( graph, source, target, as_undirected=False, ): """Checks if a path exists between a source and target node :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int source: The node index to find paths from :param int target: The index of the target node :param bool as_undirected: If set to true the graph will be treated as undirected for finding existence of a path. This only works with a :class:`~rustworkx.PyDiGraph` input for ``graph`` :return: True if a path exists, False if not :rtype: bool """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) has_path.register(PyDiGraph, digraph_has_path) has_path.register(PyGraph, graph_has_path) @functools.singledispatch def all_pairs_dijkstra_shortest_paths(graph, edge_cost_fn): """For each node in the graph, finds the shortest paths to all others. This function will generate the shortest path from all nodes in the graph using Dijkstra's algorithm. This function is multithreaded and will run launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param edge_cost_fn: A callable object that acts as a weight function for an edge. It will accept a single positional argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :return: A read-only dictionary of paths. The keys are source node indices and the values are a dict of target node indices and a list of node indices making the path. For example:: { 0: {1: [0, 1], 2: [0, 1, 2]}, 1: {2: [1, 2]}, 2: {0: [2, 0]}, } :rtype: AllPairsPathMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_pairs_dijkstra_shortest_paths.register(PyDiGraph, digraph_all_pairs_dijkstra_shortest_paths) all_pairs_dijkstra_shortest_paths.register(PyGraph, graph_all_pairs_dijkstra_shortest_paths) @functools.singledispatch def all_pairs_all_simple_paths(graph, min_depth=None, cutoff=None): """Return all the simple paths between all pairs of nodes in the graph This function is multithreaded and will launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param graph: The graph to find all simple paths in. This can be a :class:`~rustworkx.PyGraph` or a :class:`~rustworkx.PyDiGraph` :param int min_depth: The minimum depth of the path to include in the output list of paths. By default all paths are included regardless of depth, setting to 0 will behave like the default. :param int cutoff: The maximum depth of path to include in the output list of paths. By default includes all paths regardless of depth, setting to 0 will behave like default. :returns: A mapping of source node indices to a mapping of target node indices to a list of paths between the source and target nodes. :rtype: AllPairsMultiplePathMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_pairs_all_simple_paths.register(PyDiGraph, digraph_all_pairs_all_simple_paths) all_pairs_all_simple_paths.register(PyGraph, graph_all_pairs_all_simple_paths) @functools.singledispatch def all_pairs_dijkstra_path_lengths(graph, edge_cost_fn): """For each node in the graph, calculates the lengths of the shortest paths to all others. This function will generate the shortest path lengths from all nodes in the graph using Dijkstra's algorithm. This function is multithreaded and will launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param edge_cost_fn: A callable object that acts as a weight function for an edge. It will accept a single positional argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :return: A read-only dictionary of path lengths. The keys are the source node indices and the values are a dict of the target node and the length of the shortest path to that node. For example:: { 0: {1: 2.0, 2: 2.0}, 1: {2: 1.0}, 2: {0: 1.0}, } :rtype: AllPairsPathLengthMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_pairs_dijkstra_path_lengths.register(PyDiGraph, digraph_all_pairs_dijkstra_path_lengths) all_pairs_dijkstra_path_lengths.register(PyGraph, graph_all_pairs_dijkstra_path_lengths) @functools.singledispatch def dijkstra_shortest_path_lengths(graph, node, edge_cost_fn, goal=None): """Compute the lengths of the shortest paths for a graph object using Dijkstra's algorithm. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int node: The node index to use as the source for finding the shortest paths from :param edge_cost_fn: A python callable that will take in 1 parameter, an edge's data object and will return a float that represents the cost/weight of that edge. It must be non-negative :param int goal: An optional node index to use as the end of the path. When specified the traversal will stop when the goal is reached and the output dictionary will only have a single entry with the length of the shortest path to the goal node. :returns: A dictionary of the shortest paths from the provided node where the key is the node index of the end of the path and the value is the cost/sum of the weights of path :rtype: dict """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) dijkstra_shortest_path_lengths.register(PyDiGraph, digraph_dijkstra_shortest_path_lengths) dijkstra_shortest_path_lengths.register(PyGraph, graph_dijkstra_shortest_path_lengths) @functools.singledispatch def k_shortest_path_lengths(graph, start, k, edge_cost, goal=None): """Compute the length of the kth shortest path Computes the lengths of the kth shortest path from ``start`` to every reachable node. Computes in :math:`O(k * (|E| + |V|*log(|V|)))` time (average). :param graph: The graph to find the shortest paths in. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int start: The node index to find the shortest paths from :param int k: The kth shortest path to find the lengths of :param edge_cost: A python callable that will receive an edge payload and return a float for the cost of that eedge :param int goal: An optional goal node index, if specified the output dictionary :returns: A dict of lengths where the key is the destination node index and the value is the length of the path. :rtype: dict """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) k_shortest_path_lengths.register(PyDiGraph, digraph_k_shortest_path_lengths) k_shortest_path_lengths.register(PyGraph, graph_k_shortest_path_lengths) @functools.singledispatch def dfs_edges(graph, source=None): """Get an edge list of the tree edges from a depth-first traversal The pseudo-code for the DFS algorithm is listed below. The output contains the tree edges found by the procedure. :: DFS(G, v) let S be a stack label v as discovered PUSH(S, (v, iterator of G.neighbors(v))) while (S != Ø) let (v, iterator) := LAST(S) if hasNext(iterator) then w := next(iterator) if w is not labeled as discovered then label w as discovered # (v, w) is a tree edge PUSH(S, (w, iterator of G.neighbors(w))) else POP(S) end while .. note:: If the input is an undirected graph with a single connected component, the output of this function is a spanning tree. :param graph: The graph to get the DFS edge list from. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int source: An optional node index to use as the starting node for the depth-first search. The edge list will only return edges in the components reachable from this index. If this is not specified then a source will be chosen arbitrarly and repeated until all components of the graph are searched. :returns: A list of edges as a tuple of the form ``(source, target)`` in depth-first order :rtype: EdgeList """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) dfs_edges.register(PyDiGraph, digraph_dfs_edges) dfs_edges.register(PyGraph, graph_dfs_edges) @functools.singledispatch def is_isomorphic( first, second, node_matcher=None, edge_matcher=None, id_order=True, call_limit=None, ): """Determine if 2 graphs are isomorphic This checks if 2 graphs are isomorphic both structurally and also comparing the node and edge data using the provided matcher functions. The matcher functions take in 2 data objects and will compare them. A simple example that checks if they're just equal would be:: graph_a = rustworkx.PyGraph() graph_b = rustworkx.PyGraph() rustworkx.is_isomorphic(graph_a, graph_b, lambda x, y: x == y) .. note:: For better performance on large graphs, consider setting `id_order=False`. :param first: The first graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param second: The second graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. It should be the same type as the first graph. :param callable node_matcher: A python callable object that takes 2 positional one for each node data object. If the return of this function evaluates to True then the nodes passed to it are viewed as matching. :param callable edge_matcher: A python callable object that takes 2 positional one for each edge data object. If the return of this function evaluates to True then the edges passed to it are viewed as matching. :param bool id_order: If set to ``False`` this function will use a heuristic matching order based on [VF2]_ paper. Otherwise it will default to matching the nodes in order specified by their ids. :param int call_limit: An optional bound on the number of states that VF2 algorithm visits while searching for a solution. If it exceeds this limit, the algorithm will stop and return ``False``. :returns: ``True`` if the 2 graphs are isomorphic, ``False`` if they are not. :rtype: bool .. [VF2] VF2++ An Improved Subgraph Isomorphism Algorithm by Alpár Jüttner and Péter Madarasi """ raise TypeError("Invalid Input Type %s for graph" % type(first)) is_isomorphic.register(PyDiGraph, digraph_is_isomorphic) is_isomorphic.register(PyGraph, graph_is_isomorphic) @functools.singledispatch def is_isomorphic_node_match(first, second, matcher, id_order=True): """Determine if 2 graphs are isomorphic This checks if 2 graphs are isomorphic both structurally and also comparing the node data using the provided matcher function. The matcher function takes in 2 node data objects and will compare them. A simple example that checks if they're just equal would be:: graph_a = rustworkx.PyDAG() graph_b = rustworkx.PyDAG() rustworkx.is_isomorphic_node_match(graph_a, graph_b, lambda x, y: x == y) .. note:: For better performance on large graphs, consider setting `id_order=False`. :param first: The first graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param second: The second graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. It should be the same type as the first graph. :param callable matcher: A python callable object that takes 2 positional one for each node data object. If the return of this function evaluates to True then the nodes passed to it are vieded as matching. :param bool id_order: If set to ``False`` this function will use a heuristic matching order based on [VF2]_ paper. Otherwise it will default to matching the nodes in order specified by their ids. :returns: ``True`` if the 2 graphs are isomorphic ``False`` if they are not. :rtype: bool """ raise TypeError("Invalid Input Type %s for graph" % type(first)) is_isomorphic_node_match.register( PyDiGraph, functools.partial(digraph_is_isomorphic, edge_matcher=None) ) is_isomorphic_node_match.register( PyGraph, functools.partial(graph_is_isomorphic, edge_matcher=None) ) @functools.singledispatch def is_subgraph_isomorphic( first, second, node_matcher=None, edge_matcher=None, id_order=False, induced=True, call_limit=None, ): """Determine if 2 graphs are subgraph isomorphic This checks if 2 graphs are subgraph isomorphic both structurally and also comparing the node and edge data using the provided matcher functions. The matcher functions take in 2 data objects and will compare them. Since there is an ambiguity in the term 'subgraph', do note that we check for an node-induced subgraph if argument `induced` is set to `True`. If it is set to `False`, we check for a non induced subgraph, meaning the second graph can have fewer edges than the subgraph of the first. By default it's `True`. A simple example that checks if they're just equal would be:: graph_a = rustworkx.PyGraph() graph_b = rustworkx.PyGraph() rustworkx.is_subgraph_isomorphic(graph_a, graph_b, lambda x, y: x == y) :param first: The first graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param second: The second graph to compare. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. It should be the same type as the first graph. :param callable node_matcher: A python callable object that takes 2 positional one for each node data object. If the return of this function evaluates to True then the nodes passed to it are viewed as matching. :param callable edge_matcher: A python callable object that takes 2 positional one for each edge data object. If the return of this function evaluates to True then the edges passed to it are viewed as matching. :param bool id_order: If set to ``True`` this function will match the nodes in order specified by their ids. Otherwise it will default to a heuristic matching order based on [VF2]_ paper. :param bool induced: If set to ``True`` this function will check the existence of a node-induced subgraph of first isomorphic to second graph. Default: ``True``. :param int call_limit: An optional bound on the number of states that VF2 algorithm visits while searching for a solution. If it exceeds this limit, the algorithm will stop and return ``False``. :returns: ``True`` if there is a subgraph of `first` isomorphic to `second` , ``False`` if there is not. :rtype: bool """ raise TypeError("Invalid Input Type %s for graph" % type(first)) is_subgraph_isomorphic.register(PyDiGraph, digraph_is_subgraph_isomorphic) is_subgraph_isomorphic.register(PyGraph, graph_is_subgraph_isomorphic) @functools.singledispatch def transitivity(graph): """Compute the transitivity of a graph. This function is multithreaded and will run launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. .. note:: The function implicitly assumes that there are no parallel edges or self loops. It may produce incorrect/unexpected results if the input graph has self loops or parallel edges. :param graph: The graph to be used. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :returns: Transitivity of the graph. :rtype: float raise TypeError("Invalid Input Type %s for graph" % type(graph)) """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) transitivity.register(PyDiGraph, digraph_transitivity) transitivity.register(PyGraph, graph_transitivity) @functools.singledispatch def core_number(graph): """Return the core number for each node in the graph. A k-core is a maximal subgraph that contains nodes of degree k or more. .. note:: The function implicitly assumes that there are no parallel edges or self loops. It may produce incorrect/unexpected results if the input graph has self loops or parallel edges. :param graph: The graph to get core numbers. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :returns: A dictionary keyed by node index to the core number :rtype: dict raise TypeError("Invalid Input Type %s for graph" % type(graph)) """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) core_number.register(PyDiGraph, digraph_core_number) core_number.register(PyGraph, graph_core_number) @functools.singledispatch def complement(graph): """Compute the complement of a graph. :param graph: The graph to be used, can be either a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :returns: The complement of the graph. :rtype: :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` .. note:: Parallel edges and self-loops are never created, even if the ``multigraph`` is set to ``True`` """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) complement.register(PyDiGraph, digraph_complement) complement.register(PyGraph, graph_complement) @functools.singledispatch def random_layout(graph, center=None, seed=None): """Generate a random layout :param PyGraph graph: The graph to generate the layout for :param tuple center: An optional center position. This is a 2 tuple of two ``float`` values for the center position :param int seed: An optional seed to set for the random number generator. :returns: The random layout of the graph. :rtype: Pos2DMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) random_layout.register(PyDiGraph, digraph_random_layout) random_layout.register(PyGraph, graph_random_layout) @functools.singledispatch def spring_layout( graph, pos=None, fixed=None, k=None, repulsive_exponent=2, adaptive_cooling=True, num_iter=50, tol=1e-6, weight_fn=None, default_weight=1, scale=1, center=None, seed=None, ): """ Position nodes using Fruchterman-Reingold force-directed algorithm. The algorithm simulates a force-directed representation of the network treating edges as springs holding nodes close, while treating nodes as repelling objects, sometimes called an anti-gravity force. Simulation continues until the positions are close to an equilibrium. :param graph: Graph to be used. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param dict pos: Initial node positions as a dictionary with node ids as keys and values as a coordinate list. If ``None``, then use random initial positions. (``default=None``) :param set fixed: Nodes to keep fixed at initial position. Error raised if fixed specified and ``pos`` is not. (``default=None``) :param float k: Optimal distance between nodes. If ``None`` the distance is set to :math:`\\frac{1}{\\sqrt{n}}` where :math:`n` is the number of nodes. Increase this value to move nodes farther apart. (``default=None``) :param int repulsive_exponent: Repulsive force exponent. (``default=2``) :param bool adaptive_cooling: Use an adaptive cooling scheme. If set to ``False``, a linear cooling scheme is used. (``default=True``) :param int num_iter: Maximum number of iterations. (``default=50``) :param float tol: Threshold for relative error in node position changes. The iteration stops if the error is below this threshold. (``default = 1e-6``) :param weight_fn: An optional weight function for an edge. It will accept a single argument, the edge's weight object and will return a float which will be used to represent the weight of the edge. :param float (default=1) default_weight: If ``weight_fn`` isn't specified this optional float value will be used for the weight/cost of each edge :param float|None scale: Scale factor for positions. Not used unless fixed is None. If scale is ``None``, no re-scaling is performed. (``default=1.0``) :param list center: Coordinate pair around which to center the layout. Not used unless fixed is ``None``. (``default=None``) :param int seed: An optional seed to use for the random number generator :returns: A dictionary of positions keyed by node id. :rtype: dict """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) spring_layout.register(PyDiGraph, digraph_spring_layout) spring_layout.register(PyGraph, graph_spring_layout) def networkx_converter(graph, keep_attributes: bool = False): """Convert a networkx graph object into a rustworkx graph object. .. note:: networkx is **not** a dependency of rustworkx and this function is provided as a convenience method for users of both networkx and rustworkx. This function will not work unless you install networkx independently. :param networkx.Graph graph: The networkx graph to convert. :param bool keep_attributes: If ``True``, add networkx node attributes to the data payload in the nodes of the output rustworkx graph. When set to ``True``, the node data payloads in the output rustworkx graph object will be dictionaries with the node attributes from the input networkx graph where the ``"__networkx_node__"`` key contains the node from the input networkx graph. :returns: A rustworkx graph, either a :class:`~rustworkx.PyDiGraph` or a :class:`~rustworkx.PyGraph` based on whether the input graph is directed or not. :rtype: :class:`~rustworkx.PyDiGraph` or :class:`~rustworkx.PyGraph` """ if graph.is_directed(): new_graph = PyDiGraph(multigraph=graph.is_multigraph()) else: new_graph = PyGraph(multigraph=graph.is_multigraph()) nodes = list(graph.nodes) node_indices = dict(zip(nodes, new_graph.add_nodes_from(nodes))) new_graph.add_edges_from( [(node_indices[x[0]], node_indices[x[1]], x[2]) for x in graph.edges(data=True)] ) if keep_attributes: for node, node_index in node_indices.items(): attributes = graph.nodes[node] attributes["__networkx_node__"] = node new_graph[node_index] = attributes return new_graph @functools.singledispatch def bipartite_layout( graph, first_nodes, horizontal=False, scale=1, center=None, aspect_ratio=4 / 3, ): """Generate a bipartite layout of the graph :param graph: The graph to generate the layout for. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param set first_nodes: The set of node indices on the left (or top if horitontal is true) :param bool horizontal: An optional bool specifying the orientation of the layout :param float scale: An optional scaling factor to scale positions :param tuple center: An optional center position. This is a 2 tuple of two ``float`` values for the center position :param float aspect_ratio: An optional number for the ratio of the width to the height of the layout. :returns: The bipartite layout of the graph. :rtype: Pos2DMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) bipartite_layout.register(PyDiGraph, digraph_bipartite_layout) bipartite_layout.register(PyGraph, graph_bipartite_layout) @functools.singledispatch def circular_layout(graph, scale=1, center=None): """Generate a circular layout of the graph :param graph: The graph to generate the layout for. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param float scale: An optional scaling factor to scale positions :param tuple center: An optional center position. This is a 2 tuple of two ``float`` values for the center position :returns: The circular layout of the graph. :rtype: Pos2DMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) circular_layout.register(PyDiGraph, digraph_circular_layout) circular_layout.register(PyGraph, graph_circular_layout) @functools.singledispatch def shell_layout(graph, nlist=None, rotate=None, scale=1, center=None): """ Generate a shell layout of the graph :param graph: The graph to generate the layout for. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param list nlist: The list of lists of indices which represents each shell :param float rotate: Angle (in radians) by which to rotate the starting position of each shell relative to the starting position of the previous shell :param float scale: An optional scaling factor to scale positions :param tuple center: An optional center position. This is a 2 tuple of two ``float`` values for the center position :returns: The shell layout of the graph. :rtype: Pos2DMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) shell_layout.register(PyDiGraph, digraph_shell_layout) shell_layout.register(PyGraph, graph_shell_layout) @functools.singledispatch def spiral_layout(graph, scale=1, center=None, resolution=0.35, equidistant=False): """ Generate a spiral layout of the graph :param graph: The graph to generate the layout for. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param float scale: An optional scaling factor to scale positions :param tuple center: An optional center position. This is a 2 tuple of two ``float`` values for the center position :param float resolution: The compactness of the spiral layout returned. Lower values result in more compressed spiral layouts. :param bool equidistant: If true, nodes will be plotted equidistant from each other. :returns: The spiral layout of the graph. :rtype: Pos2DMapping """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) spiral_layout.register(PyDiGraph, digraph_spiral_layout) spiral_layout.register(PyGraph, graph_spiral_layout) @functools.singledispatch def num_shortest_paths_unweighted(graph, source): """Get the number of unweighted shortest paths from a source node :param PyDiGraph graph: The graph to find the number of shortest paths on :param int source: The source node to find the shortest paths from :returns: A mapping of target node indices to the number of shortest paths from ``source`` to that node. If there is no path from ``source`` to a node in the graph that node will not be preset in the output mapping. :rtype: NodesCountMapping """ raise TypeError("Invalid input type %s for graph" % type(graph)) num_shortest_paths_unweighted.register(PyDiGraph, digraph_num_shortest_paths_unweighted) num_shortest_paths_unweighted.register(PyGraph, graph_num_shortest_paths_unweighted) @functools.singledispatch def betweenness_centrality(graph, normalized=True, endpoints=False, parallel_threshold=50): r"""Returns the betweenness centrality of each node in the graph. Betweenness centrality of a node :math:`v` is the sum of the fraction of all-pairs shortest paths that pass through :math`v` .. math:: c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)} where :math:`V` is the set of nodes, :math:`\sigma(s, t)` is the number of shortest :math`(s, t)` paths, and :math:`\sigma(s, t|v)` is the number of those paths passing through some node :math:`v` other than :math:`s, t`. If :math:`s = t`, :math:`\sigma(s, t) = 1`, and if :math:`v \in {s, t}`, :math:`\sigma(s, t|v) = 0` The algorithm used in this function is based on: Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001. This function is multithreaded and will run in parallel if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 50). If the function will be running in parallel the env var ``RAYON_NUM_THREADS`` can be used to adjust how many threads will be used. See Also -------- edge_betweenness_centrality :param PyDiGraph graph: The input graph :param bool normalized: Whether to normalize the betweenness scores by the number of distinct paths between all pairs of nodes. :param bool endpoints: Whether to include the endpoints of paths in path lengths used to compute the betweenness. :param int parallel_threshold: The number of nodes to calculate the the betweenness centrality in parallel at if the number of nodes in the graph is less than this value it will run in a single thread. The default value is 50 :returns: A dictionary mapping each node index to its betweenness centrality. :rtype: dict """ raise TypeError("Invalid input type %s for graph" % type(graph)) betweenness_centrality.register(PyDiGraph, digraph_betweenness_centrality) betweenness_centrality.register(PyGraph, graph_betweenness_centrality) @functools.singledispatch def closeness_centrality(graph, wf_improved=True): r"""Compute the closeness centrality of each node in a graph object. The closeness centrality of a node :math:`u` is defined as the reciprocal of the average shortest path distance to :math:`u` over all :math:`n-1` reachable nodes in the graph. In it's general form this can be expressed as: .. math:: C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)}, where: * :math:`d(v, u)` - the shortest-path distance between :math:`v` and :math:`u` * :math:`n` - the number of nodes that can reach :math:`u`. In the case of a graphs with more than one connected component there is an alternative improved formula that calculates the closeness centrality as "a ratio of the fraction of actors in the group who are reachable, to the average distance" [WF]_. This can be expressed as .. math:: C_{WF}(u) = \frac{n-1}{N-1} \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)}, where :math:`N` is the number of nodes in the graph. This alternative formula can be used with the ``wf_improved`` argument. :param graph: The input graph. Can either be a :class:`~retworkx.PyGraph` or :class:`~retworkx.PyDiGraph`. :param bool wf_improved: This is optional; the default is True. If True, scale by the fraction of nodes reachable. :returns: A dictionary mapping each node index to its closeness centrality. :rtype: dict .. [WF] Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Applications (Structural Analysis in the Social Sciences). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511815478 """ raise TypeError("Invalid input type %s for graph" % type(graph)) closeness_centrality.register(PyDiGraph, digraph_closeness_centrality) closeness_centrality.register(PyGraph, graph_closeness_centrality) @functools.singledispatch def edge_betweenness_centrality(graph, normalized=True, parallel_threshold=50): r"""Compute the edge betweenness centrality of all edges in a graph. Edge betweenness centrality of an edge :math:`e` is the sum of the fraction of all-pairs shortest paths that pass through :math`e` .. math:: c_B(e) = \sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)} where :math:`V` is the set of nodes, :math:`\sigma(s, t)` is the number of shortest :math:`(s, t)`-paths, and :math:`\sigma(s, t|e)` is the number of those paths passing through edge :math:`e`. The above definition and the algorithm used in this function is based on: Ulrik Brandes, On Variants of Shortest-Path Betweenness Centrality and their Generic Computation. Social Networks 30(2):136-145, 2008. This function is multithreaded and will run in parallel if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 50). If the function will be running in parallel the env var ``RAYON_NUM_THREADS`` can be used to adjust how many threads will be used. See Also -------- betweenness_centrality :param PyGraph graph: The input graph :param bool normalized: Whether to normalize the betweenness scores by the number of distinct paths between all pairs of nodes. :param int parallel_threshold: The number of nodes to calculate the edge betweenness centrality in parallel at if the number of nodes in the graph is less than this value it will run in a single thread. The default value is 50 :returns: a read-only dict-like object whose keys are edges and values are the betweenness score for each node. :rtype: EdgeCentralityMapping """ raise TypeError("Invalid input type %s for graph" % type(graph)) edge_betweenness_centrality.register(PyDiGraph, digraph_edge_betweenness_centrality) edge_betweenness_centrality.register(PyGraph, graph_edge_betweenness_centrality) @functools.singledispatch def eigenvector_centrality(graph, weight_fn=None, default_weight=1.0, max_iter=100, tol=1e-6): """Compute the eigenvector centrality of a graph. For details on the eigenvector centrality refer to: Phillip Bonacich. “Power and Centrality: A Family of Measures.” American Journal of Sociology 92(5):1170–1182, 1986 This function uses a power iteration method to compute the eigenvector and convergence is not guaranteed. The function will stop when `max_iter` iterations is reached or when the computed vector between two iterations is smaller than the error tolerance multiplied by the number of nodes. The implementation of this algorithm is based on the NetworkX `eigenvector_centrality() `__ function. In the case of multigraphs the weights of any parallel edges will be summed when computing the eigenvector centrality. :param graph: Graph to be used. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param weight_fn: An optional input callable that will be passed the edge's payload object and is expected to return a `float` weight for that edge. If this is not specified ``default_weight`` will be used as the weight for every edge in ``graph`` :param float default_weight: If ``weight_fn`` is not set the default weight value to use for the weight of all edges :param int max_iter: The maximum number of iterations in the power method. If not specified a default value of 100 is used. :param float tol: The error tolerance used when checking for convergence in the power method. If this is not specified default value of 1e-6 is used. :returns: a read-only dict-like object whose keys are the node indices and values are the centrality score for that node. :rtype: CentralityMapping """ raise TypeError("Invalid input type %s for graph" % type(graph)) eigenvector_centrality.register(PyDiGraph, digraph_eigenvector_centrality) eigenvector_centrality.register(PyGraph, graph_eigenvector_centrality) @functools.singledispatch def katz_centrality( graph, alpha=0.1, beta=1.0, weight_fn=None, default_weight=1.0, max_iter=100, tol=1e-6 ): """Compute the Katz centrality of a graph. For details on the Katz centrality refer to: Leo Katz. “A New Status Index Derived from Sociometric Index.” Psychometrika 18(1):39–43, 1953 This function uses a power iteration method to compute the eigenvector and convergence is not guaranteed. The function will stop when `max_iter` iterations is reached or when the computed vector between two iterations is smaller than the error tolerance multiplied by the number of nodes. The implementation of this algorithm is based on the NetworkX `katz_centrality() `__ function. In the case of multigraphs the weights of any parallel edges will be summed when computing the Katz centrality. :param graph: Graph to be used. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`. :param float alpha: Attenuation factor. If this is not specified default value of 0.1 is used. :param float | dict beta: Immediate neighbourhood weights. If a float is provided, the neighbourhood weight is used for all nodes. If a dictionary is provided, it must contain all node indices. If beta is not specified, a default value of 1.0 is used. :param weight_fn: An optional input callable that will be passed the edge's payload object and is expected to return a `float` weight for that edge. If this is not specified ``default_weight`` will be used as the weight for every edge in ``graph`` :param float default_weight: If ``weight_fn`` is not set the default weight value to use for the weight of all edges :param int max_iter: The maximum number of iterations in the power method. If not specified a default value of 100 is used. :param float tol: The error tolerance used when checking for convergence in the power method. If this is not specified default value of 1e-6 is used. :returns: a read-only dict-like object whose keys are the node indices and values are the centrality score for that node. :rtype: CentralityMapping """ raise TypeError("Invalid input type %s for graph" % type(graph)) katz_centrality.register(PyDiGraph, digraph_katz_centrality) katz_centrality.register(PyGraph, graph_katz_centrality) @functools.singledispatch def vf2_mapping( first, second, node_matcher=None, edge_matcher=None, id_order=True, subgraph=False, induced=True, call_limit=None, ): """ Return an iterator over all vf2 mappings between two graphs. This funcion will run the vf2 algorithm used from :func:`~rustworkx.is_isomorphic` and :func:`~rustworkx.is_subgraph_isomorphic` but instead of returning a boolean it will return an iterator over all possible mapping of node ids found from ``first`` to ``second``. If the graphs are not isomorphic then the iterator will be empty. A simple example that retrieves one mapping would be:: graph_a = rustworkx.generators.path_graph(3) graph_b = rustworkx.generators.path_graph(2) vf2 = rustworkx.vf2_mapping(graph_a, graph_b, subgraph=True) try: mapping = next(vf2) except StopIteration: pass :param first: The first graph to find the mapping for :param second: The second graph to find the mapping for :param node_matcher: An optional python callable object that takes 2 positional arguments, one for each node data object in either graph. If the return of this function evaluates to True then the nodes passed to it are viewed as matching. :param edge_matcher: A python callable object that takes 2 positional one for each edge data object. If the return of this function evaluates to True then the edges passed to it are viewed as matching. :param bool id_order: If set to ``False`` this function will use a heuristic matching order based on [VF2]_ paper. Otherwise it will default to matching the nodes in order specified by their ids. :param bool subgraph: If set to ``True`` the function will return the subgraph isomorphic found between the graphs. :param bool induced: If set to ``True`` this function will check the existence of a node-induced subgraph of first isomorphic to second graph. Default: ``True``. :param int call_limit: An optional bound on the number of states that VF2 algorithm visits while searching for a solution. If it exceeds this limit, the algorithm will stop. Default: ``None``. :returns: An iterator over dicitonaries of node indices from ``first`` to node indices in ``second`` representing the mapping found. :rtype: Iterable[NodeMap] """ raise TypeError("Invalid Input Type %s for graph" % type(first)) vf2_mapping.register(PyDiGraph, digraph_vf2_mapping) vf2_mapping.register(PyGraph, graph_vf2_mapping) @functools.singledispatch def union( first, second, merge_nodes=False, merge_edges=False, ): """Return a new graph by forming a union from two input graph objects The algorithm in this function operates in three phases: 1. Add all the nodes from ``second`` into ``first``. operates in :math:`\\mathcal{O}(n_2)`, with :math:`n_2` being number of nodes in ``second``. 2. Merge nodes from ``second`` over ``first`` given that: - The ``merge_nodes`` is ``True``. operates in :math:`\\mathcal{O}(n_1 n_2)`, with :math:`n_1` being the number of nodes in ``first`` and :math:`n_2` the number of nodes in ``second`` - The respective node in ``second`` and ``first`` share the same weight/data payload. 3. Adds all the edges from ``second`` to ``first``. If the ``merge_edges`` parameter is ``True`` and the respective edge in ``second`` and ``first`` share the same weight/data payload they will be merged together. :param first: The first graph object :param second: The second graph object :param bool merge_nodes: If set to ``True`` nodes will be merged between ``second`` and ``first`` if the weights are equal. Default: ``False``. :param bool merge_edges: If set to ``True`` edges will be merged between ``second`` and ``first`` if the weights are equal. Default: ``False``. :returns: A new graph object that is the union of ``second`` and ``first``. It's worth noting the weight/data payload objects are passed by reference from ``first`` and ``second`` to this new object. :rtype: :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` """ raise TypeError("Invalid Input Type %s for graph" % type(first)) union.register(PyDiGraph, digraph_union) union.register(PyGraph, graph_union) @functools.singledispatch def tensor_product( first, second, ): """Return a new graph by forming the tensor product from two input graph objects :param first: The first graph object :param second: The second graph object :returns: A new graph object that is the tensor product of ``second`` and ``first``. It's worth noting the weight/data payload objects are passed by reference from ``first`` and ``second`` to this new object. A read-only dictionary of the product of nodes is also returned. The keys are a tuple where the first element is a node of the first graph and the second element is a node of the second graph, and the values are the map of those elements to node indices in the product graph. For example:: { (0, 0): 0, (0, 1): 1, } :rtype: Tuple[:class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`, :class:`~rustworkx.ProductNodeMap`] """ raise TypeError("Invalid Input Type %s for graph" % type(first)) tensor_product.register(PyDiGraph, digraph_tensor_product) tensor_product.register(PyGraph, graph_tensor_product) @functools.singledispatch def cartesian_product( first, second, ): """Return a new graph by forming the cartesian product from two input graph objects :param first: The first graph object :param second: The second graph object :returns: A new graph object that is the union of ``second`` and ``first``. It's worth noting the weight/data payload objects are passed by reference from ``first`` and ``second`` to this new object. A read-only dictionary of the product of nodes is also returned. The keys are a tuple where the first element is a node of the first graph and the second element is a node of the second graph, and the values are the map of those elements to node indices in the product graph. For example:: { (0, 0): 0, (0, 1): 1, } :rtype: Tuple[:class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph`, :class:`~rustworkx.ProductNodeMap`] """ raise TypeError("Invalid Input Type %s for graph" % type(first)) cartesian_product.register(PyDiGraph, digraph_cartesian_product) cartesian_product.register(PyGraph, graph_cartesian_product) @functools.singledispatch def bfs_search(graph, source, visitor): """Breadth-first traversal of a directed/undirected graph. The pseudo-code for the BFS algorithm is listed below, with the annotated event points, for which the given visitor object will be called with the appropriate method. :: BFS(G, s) for each vertex u in V color[u] := WHITE end for color[s] := GRAY EQUEUE(Q, s) discover vertex s while (Q != Ø) u := DEQUEUE(Q) for each vertex v in Adj[u] (u,v) is a tree edge if (color[v] = WHITE) color[v] = GRAY else (u,v) is a non - tree edge if (color[v] = GRAY) (u,v) has a gray target ... else if (color[v] = BLACK) (u,v) has a black target ... end for color[u] := BLACK finish vertex u end while If an exception is raised inside the callback function, the graph traversal will be stopped immediately. You can exploit this to exit early by raising a :class:`~rustworkx.visit.StopSearch` exception, in which case the search function will return but without raising back the exception. You can also prune part of the search tree by raising :class:`~rustworkx.visit.PruneSearch`. In the following example we keep track of the tree edges: .. jupyter-execute:: import rustworkx as rx from rustworkx.visit import BFSVisitor class TreeEdgesRecorder(BFSVisitor): def __init__(self): self.edges = [] def tree_edge(self, edge): self.edges.append(edge) graph = rx.PyDiGraph() graph.extend_from_edge_list([(1, 3), (0, 1), (2, 1), (0, 2)]) vis = TreeEdgesRecorder() rx.bfs_search(graph, [0], vis) print('Tree edges:', vis.edges) .. note:: Graph can **not** be mutated while traversing. :param graph: The graph to be used. This can be a :class:`~rustworkx.PyGraph` or a :class:`~rustworkx.PyDiGraph` :param List[int] source: An optional list of node indices to use as the starting nodes for the breadth-first search. If this is not specified then a source will be chosen arbitrarly and repeated until all components of the graph are searched. :param visitor: A visitor object that is invoked at the event points inside the algorithm. This should be a subclass of :class:`~rustworkx.visit.BFSVisitor`. """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) bfs_search.register(PyDiGraph, digraph_bfs_search) bfs_search.register(PyGraph, graph_bfs_search) @functools.singledispatch def dfs_search(graph, source, visitor): """Depth-first traversal of a directed/undirected graph. The pseudo-code for the DFS algorithm is listed below, with the annotated event points, for which the given visitor object will be called with the appropriate method. :: DFS(G) for each vertex u in V color[u] := WHITE initialize vertex u end for time := 0 call DFS-VISIT(G, source) start vertex s DFS-VISIT(G, u) color[u] := GRAY discover vertex u for each v in Adj[u] examine edge (u,v) if (color[v] = WHITE) (u,v) is a tree edge all DFS-VISIT(G, v) else if (color[v] = GRAY) (u,v) is a back edge ... else if (color[v] = BLACK) (u,v) is a cross or forward edge ... end for color[u] := BLACK finish vertex u If an exception is raised inside the callback function, the graph traversal will be stopped immediately. You can exploit this to exit early by raising a :class:`~rustworkx.visit.StopSearch` exception. You can also prune part of the search tree by raising :class:`~rustworkx.visit.PruneSearch`. In the following example we keep track of the tree edges: .. jupyter-execute:: import rustworkx as rx from rustworkx.visit import DFSVisitor class TreeEdgesRecorder(DFSVisitor): def __init__(self): self.edges = [] def tree_edge(self, edge): self.edges.append(edge) graph = rx.PyGraph() graph.extend_from_edge_list([(1, 3), (0, 1), (2, 1), (0, 2)]) vis = TreeEdgesRecorder() rx.dfs_search(graph, [0], vis) print('Tree edges:', vis.edges) .. note:: Graph can *not* be mutated while traversing. :param PyGraph graph: The graph to be used. :param List[int] source: An optional list of node indices to use as the starting nodes for the depth-first search. If this is not specified then a source will be chosen arbitrarly and repeated until all components of the graph are searched. :param visitor: A visitor object that is invoked at the event points inside the algorithm. This should be a subclass of :class:`~rustworkx.visit.DFSVisitor`. """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) dfs_search.register(PyDiGraph, digraph_dfs_search) dfs_search.register(PyGraph, graph_dfs_search) @functools.singledispatch def dijkstra_search(graph, source, weight_fn, visitor): """Dijkstra traversal of a graph. The pseudo-code for the Dijkstra algorithm is listed below, with the annotated event points, for which the given visitor object will be called with the appropriate method. :: DIJKSTRA(G, source, weight) for each vertex u in V d[u] := infinity p[u] := u end for d[source] := 0 INSERT(Q, source) while (Q != Ø) u := EXTRACT-MIN(Q) discover vertex u for each vertex v in Adj[u] examine edge (u,v) if (weight[(u,v)] + d[u] < d[v]) edge (u,v) relaxed d[v] := weight[(u,v)] + d[u] p[v] := u DECREASE-KEY(Q, v) else edge (u,v) not relaxed ... if (d[v] was originally infinity) INSERT(Q, v) end for finish vertex u end while If an exception is raised inside the callback function, the graph traversal will be stopped immediately. You can exploit this to exit early by raising a :class:`~rustworkx.visit.StopSearch` exception, in which case the search function will return but without raising back the exception. You can also prune part of the search tree by raising :class:`~rustworkx.visit.PruneSearch`. .. note:: Graph can **not** be mutated while traversing. :param graph: The graph to be used. This can be a :class:`~rustworkx.PyGraph` or a :class:`~rustworkx.PyDiGraph`. :param List[int] source: An optional list of node indices to use as the starting nodes for the dijkstra search. If this is not specified then a source will be chosen arbitrarly and repeated until all components of the graph are searched. :param weight_fn: An optional weight function for an edge. It will accept a single argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge. If not specified, a default value of cost ``1.0`` will be used for each edge. :param visitor: A visitor object that is invoked at the event points inside the algorithm. This should be a subclass of :class:`~rustworkx.visit.DijkstraVisitor`. """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) dijkstra_search.register(PyDiGraph, digraph_dijkstra_search) dijkstra_search.register(PyGraph, graph_dijkstra_search) @functools.singledispatch def bellman_ford_shortest_paths( graph, source, target=None, weight_fn=None, default_weight=1.0, as_undirected=False, ): """Find the shortest path from a node This function will generate the shortest path from a source node using the Bellman-Ford algorithm wit the SPFA heuristic. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int source: The node index to find paths from :param int target: An optional target to find a path to :param weight_fn: An optional weight function for an edge. It will accept a single argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :param float default_weight: If ``weight_fn`` isn't specified this optional float value will be used for the weight/cost of each edge. :param bool as_undirected: If set to true the graph will be treated as undirected for finding the shortest path. This only works with a :class:`~rustworkx.PyDiGraph` input for ``graph`` :return: A read-only dictionary of paths. The keys are destination node indices and the dict values are lists of node indices making the path. :rtype: PathMapping :raises: :class:`~rustworkx.NegativeCycle`: when there is a negative cycle and the shortest path is not defined """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) bellman_ford_shortest_paths.register(PyDiGraph, digraph_bellman_ford_shortest_paths) bellman_ford_shortest_paths.register(PyGraph, graph_bellman_ford_shortest_paths) @functools.singledispatch def bellman_ford_shortest_path_lengths(graph, node, edge_cost_fn, goal=None): """Compute the lengths of the shortest paths for a graph object using the Bellman-Ford algorithm with the SPFA heuristic. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param int node: The node index to use as the source for finding the shortest paths from :param edge_cost_fn: A python callable that will take in 1 parameter, an edge's data object and will return a float that represents the cost/weight of that edge. It can be negative. :param int goal: An optional node index to use as the end of the path. When specified the output dictionary will only have a single entry with the length of the shortest path to the goal node. :returns: A read-only dictionary of the shortest paths from the provided node where the key is the node index of the end of the path and the value is the cost/sum of the weights of path :rtype: PathLengthMapping :raises: :class:`~rustworkx.NegativeCycle`: when there is a negative cycle and the shortest path is not defined """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) bellman_ford_shortest_path_lengths.register(PyDiGraph, digraph_bellman_ford_shortest_path_lengths) bellman_ford_shortest_path_lengths.register(PyGraph, graph_bellman_ford_shortest_path_lengths) @functools.singledispatch def all_pairs_bellman_ford_path_lengths(graph, edge_cost_fn): """For each node in the graph, calculates the lengths of the shortest paths to all others. This function will generate the shortest path lengths from all nodes in the graph using the Bellman-Ford algorithm. This function is multithreaded and will launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param edge_cost_fn: A callable object that acts as a weight function for an edge. It will accept a single positional argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :return: A read-only dictionary of path lengths. The keys are the source node indices and the values are a dict of the target node and the length of the shortest path to that node. For example:: { 0: {1: 2.0, 2: 2.0}, 1: {2: 1.0}, 2: {0: 1.0}, } :rtype: AllPairsPathLengthMapping :raises: :class:`~rustworkx.NegativeCycle`: when there is a negative cycle and the shortest path is not defined """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_pairs_bellman_ford_path_lengths.register(PyDiGraph, digraph_all_pairs_bellman_ford_path_lengths) all_pairs_bellman_ford_path_lengths.register(PyGraph, graph_all_pairs_bellman_ford_path_lengths) @functools.singledispatch def all_pairs_bellman_ford_shortest_paths(graph, edge_cost_fn): """For each node in the graph, finds the shortest paths to all others. This function will generate the shortest path from all nodes in the graph using the Bellman-Ford algorithm. This function is multithreaded and will run launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param graph: The input graph to use. Can either be a :class:`~rustworkx.PyGraph` or :class:`~rustworkx.PyDiGraph` :param edge_cost_fn: A callable object that acts as a weight function for an edge. It will accept a single positional argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :return: A read-only dictionary of paths. The keys are source node indices and the values are a dict of target node indices and a list of node indices making the path. For example:: { 0: {1: [0, 1], 2: [0, 1, 2]}, 1: {2: [1, 2]}, 2: {0: [2, 0]}, } :rtype: AllPairsPathMapping :raises: :class:`~rustworkx.NegativeCycle`: when there is a negative cycle and the shortest path is not defined """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_pairs_bellman_ford_shortest_paths.register( PyDiGraph, digraph_all_pairs_bellman_ford_shortest_paths ) all_pairs_bellman_ford_shortest_paths.register(PyGraph, graph_all_pairs_bellman_ford_shortest_paths) @functools.singledispatch def node_link_json(graph, path=None, graph_attrs=None, node_attrs=None, edge_attrs=None): """Generate a JSON object representing a graph in a node-link format :param graph: The graph to generate the JSON for. Can either be a :class:`~retworkx.PyGraph` or :class:`~retworkx.PyDiGraph`. :param str path: An optional path to write the JSON output to. If specified the function will not return anything and instead will write the JSON to the file specified. :param graph_attrs: An optional callable that will be passed the :attr:`~.PyGraph.attrs` attribute of the graph and is expected to return a dictionary of string keys to string values representing the graph attributes. This dictionary will be included as attributes in the output JSON. If anything other than a dictionary with string keys and string values is returned an exception will be raised. :param node_attrs: An optional callable that will be passed the node data payload for each node in the graph and is expected to return a dictionary of string keys to string values representing the data payload. This dictionary will be used as the ``data`` field for each node. :param edge_attrs: An optional callable that will be passed the edge data payload for each node in the graph and is expected to return a dictionary of string keys to string values representing the data payload. This dictionary will be used as the ``data`` field for each edge. :returns: Either the JSON string for the payload or ``None`` if ``path`` is specified :rtype: str """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) node_link_json.register(PyDiGraph, digraph_node_link_json) node_link_json.register(PyGraph, graph_node_link_json) @functools.singledispatch def longest_simple_path(graph): """Return a longest simple path in the graph This function searches computes all pairs of all simple paths and returns a path of the longest length from that set. It is roughly equivalent to running something like:: from rustworkx import all_pairs_all_simple_paths max((y.values for y in all_pairs_all_simple_paths(graph).values()), key=lambda x: len(x)) but this function will be more efficient than using ``max()`` as the search is evaluated in parallel before returning to Python. In the case of multiple paths of the same maximum length being present in the graph only one will be provided. There are no guarantees on which of the multiple longest paths will be returned (as it is determined by the parallel execution order). This is a tradeoff to improve runtime performance. If a stable return is required in such case consider using the ``max()`` equivalent above instead. This function is multithreaded and will launch a thread pool with threads equal to the number of CPUs by default. You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads. :param PyGraph graph: The graph to find the longest path in :returns: A sequence of node indices that represent the longest simple graph found in the graph. If the graph is empty ``None`` will be returned instead. :rtype: NodeIndices """ longest_simple_path.register(PyDiGraph, digraph_longest_simple_path) longest_simple_path.register(PyGraph, graph_longest_simple_path) @functools.singledispatch def isolates(graph): """Return a list of isolates in a graph object An isolate is a node without any neighbors meaning it has a degree of 0. For directed graphs this means the in-degree and out-degree are both 0. :param graph: The input graph to find isolates in :returns: A list of node indices for isolates in the graph :rtype: NodeIndices """ isolates.register(PyDiGraph, digraph_isolates) isolates.register(PyGraph, graph_isolates) @functools.singledispatch def two_color(graph): """Compute a two-coloring of a directed graph If a two coloring is not possible for the input graph (meaning it is not bipartite), ``None`` is returned. :param graph: The graph to find the coloring for :returns: If a coloring is possible return a dictionary of node indices to the color as an integer (0 or 1) :rtype: dict """ two_color.register(PyDiGraph, digraph_two_color) two_color.register(PyGraph, graph_two_color) @functools.singledispatch def is_bipartite(graph): """Determine if a given graph is bipartite :param graph: The graph to check if it's bipartite :returns: ``True`` if the graph is bipartite and ``False`` if it is not :rtype: bool """ is_bipartite.register(PyDiGraph, digraph_is_bipartite) is_bipartite.register(PyGraph, graph_is_bipartite) @functools.singledispatch def floyd_warshall_successor_and_distance( graph, weight_fn=None, default_weight=1.0, parallel_threshold=300, ): """ Find all-pairs shortest path lengths using Floyd's algorithm. Floyd's algorithm is used for finding shortest paths in dense graphs or graphs with negative weights (where Dijkstra's algorithm fails). This function is multithreaded and will launch a pool with threads equal to the number of CPUs by default if the number of nodes in the graph is above the value of ``parallel_threshold`` (it defaults to 300). You can tune the number of threads with the ``RAYON_NUM_THREADS`` environment variable. For example, setting ``RAYON_NUM_THREADS=4`` would limit the thread pool to 4 threads if parallelization was enabled. :param PyDiGraph graph: The directed graph to run Floyd's algorithm on :param weight_fn: A callable object (function, lambda, etc) which will be passed the edge object and expected to return a ``float``. This tells rustworkx/rust how to extract a numerical weight as a ``float`` for edge object. Some simple examples are:: floyd_warshall_successor_and_distance(graph, weight_fn=lambda _: 1) to return a weight of 1 for all edges. Also: floyd_warshall_successor_and_distance(graph, weight_fn=float) to cast the edge object as a float as the weight. :param as_undirected: If set to true each directed edge will be treated as bidirectional/undirected. :param int parallel_threshold: The number of nodes to execute the algorithm in parallel at. It defaults to 300, but this can be tuned :returns: A tuple of two matrices. First one is a matrix of shortest path distances between nodes. If there is no path between two nodes then the corresponding matrix entry will be ``np.inf``. Second one is a matrix of **next** nodes for given source and target. If there is no path between two nodes then the corresponding matrix entry will be the same as a target node. To reconstruct the shortest path among nodes:: def reconstruct_path(source, target, successors): path = [] if source == target: return path curr = source while curr != target: path.append(curr) curr = successors[curr, target] path.append(target) return path :rtype: (numpy.ndarray, numpy.ndarray) """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) floyd_warshall_successor_and_distance.register( PyDiGraph, digraph_floyd_warshall_successor_and_distance ) floyd_warshall_successor_and_distance.register(PyGraph, graph_floyd_warshall_successor_and_distance) @functools.singledispatch def all_shortest_paths( graph, source, target, weight_fn=None, default_weight=1.0, as_undirected=False, ): """ Find all shortest paths between two nodes This function will generate all possible shortest paths from a source node to a target using Dijkstra's algorithm. :param graph: The input graph to find the shortest paths for :param int source: The node index to find paths from :param int target: A target to find paths to :param weight_fn: An optional weight function for an edge. It will accept a single argument, the edge's weight object and will return a float which will be used to represent the weight/cost of the edge :param float default_weight: If ``weight_fn`` isn't specified this optional float value will be used for the weight/cost of each edge. :return: List of paths. Each paths are lists of node indices, starting at ``source`` and ending at ``target``. :rtype: list :raises ValueError: when an edge weight with NaN or negative value is provided. """ raise TypeError("Invalid Input Type %s for graph" % type(graph)) all_shortest_paths.register(PyDiGraph, digraph_all_shortest_paths) all_shortest_paths.register(PyGraph, graph_all_shortest_paths)