graph_tools¶
Tools for dealing with a directed graph.
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class
quantecon.graph_tools.
DiGraph
(adj_matrix, weighted=False, node_labels=None)[source]¶ Bases:
object
Class for a directed graph. It stores useful information about the graph structure such as strong connectivity [1] and periodicity [2].
Parameters: - adj_matrix : array_like(ndim=2)
Adjacency matrix representing a directed graph. Must be of shape n x n.
- weighted : bool, optional(default=False)
Whether to treat adj_matrix as a weighted adjacency matrix.
- node_labels : array_like(default=None)
Array_like of length n containing the labels associated with the nodes, which must be homogeneous in type. If None, the labels default to integers 0 through n-1.
References
[1] Strongly connected component, Wikipedia. [2] Aperiodic graph, Wikipedia. Attributes: - csgraph : scipy.sparse.csr_matrix
Compressed sparse representation of the digraph.
- is_strongly_connected : bool
Indicate whether the digraph is strongly connected.
- num_strongly_connected_components : int
The number of the strongly connected components.
- strongly_connected_components_indices : list(ndarray(int))
List of numpy arrays containing the indices of the strongly connected components.
- strongly_connected_components : list(ndarray)
List of numpy arrays containing the strongly connected components, where the nodes are annotated with their labels (if node_labels is not None).
- num_sink_strongly_connected_components : int
The number of the sink strongly connected components.
- sink_strongly_connected_components_indices : list(ndarray(int))
List of numpy arrays containing the indices of the sink strongly connected components.
- sink_strongly_connected_components : list(ndarray)
List of numpy arrays containing the sink strongly connected components, where the nodes are annotated with their labels (if node_labels is not None).
- is_aperiodic : bool
Indicate whether the digraph is aperiodic.
- period : int
The period of the digraph. Defined only for a strongly connected digraph.
- cyclic_components_indices : list(ndarray(int))
List of numpy arrays containing the indices of the cyclic components.
- cyclic_components : list(ndarray)
List of numpy arrays containing the cyclic components, where the nodes are annotated with their labels (if node_labels is not None).
Methods
subgraph
(nodes)Return the subgraph consisting of the given nodes and edges between thses nodes. -
cyclic_components
¶
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cyclic_components_indices
¶
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is_aperiodic
¶
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is_strongly_connected
¶
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node_labels
¶
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num_sink_strongly_connected_components
¶
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num_strongly_connected_components
¶
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period
¶
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scc_proj
¶
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sink_scc_labels
¶
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sink_strongly_connected_components
¶
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sink_strongly_connected_components_indices
¶
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strongly_connected_components
¶
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strongly_connected_components_indices
¶
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quantecon.graph_tools.
random_tournament_graph
(n, random_state=None)[source]¶ Return a random tournament graph [1] with n nodes.
Parameters: - n : scalar(int)
Number of nodes.
- random_state : int or np.random.RandomState, optional
Random seed (integer) or np.random.RandomState instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used.
Returns: - DiGraph
A DiGraph representing the tournament graph.
References
[1] Tournament (graph theory), Wikipedia.