112 lines
2.6 KiB
Python
112 lines
2.6 KiB
Python
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"""Attracting components."""
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import networkx as nx
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from networkx.utils.decorators import not_implemented_for
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__all__ = [
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"number_attracting_components",
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"attracting_components",
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"is_attracting_component",
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]
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@not_implemented_for("undirected")
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def attracting_components(G):
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"""Generates the attracting components in `G`.
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An attracting component in a directed graph `G` is a strongly connected
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component with the property that a random walker on the graph will never
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leave the component, once it enters the component.
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The nodes in attracting components can also be thought of as recurrent
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nodes. If a random walker enters the attractor containing the node, then
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the node will be visited infinitely often.
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To obtain induced subgraphs on each component use:
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``(G.subgraph(c).copy() for c in attracting_components(G))``
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Parameters
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----------
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G : DiGraph, MultiDiGraph
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The graph to be analyzed.
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Returns
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-------
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attractors : generator of sets
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A generator of sets of nodes, one for each attracting component of G.
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Raises
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------
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NetworkXNotImplemented
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If the input graph is undirected.
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See Also
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--------
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number_attracting_components
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is_attracting_component
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"""
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scc = list(nx.strongly_connected_components(G))
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cG = nx.condensation(G, scc)
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for n in cG:
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if cG.out_degree(n) == 0:
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yield scc[n]
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@not_implemented_for("undirected")
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def number_attracting_components(G):
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"""Returns the number of attracting components in `G`.
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Parameters
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----------
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G : DiGraph, MultiDiGraph
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The graph to be analyzed.
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Returns
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-------
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n : int
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The number of attracting components in G.
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Raises
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------
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NetworkXNotImplemented
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If the input graph is undirected.
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See Also
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--------
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attracting_components
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is_attracting_component
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"""
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return sum(1 for ac in attracting_components(G))
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@not_implemented_for("undirected")
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def is_attracting_component(G):
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"""Returns True if `G` consists of a single attracting component.
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Parameters
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----------
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G : DiGraph, MultiDiGraph
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The graph to be analyzed.
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Returns
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-------
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attracting : bool
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True if `G` has a single attracting component. Otherwise, False.
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Raises
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------
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NetworkXNotImplemented
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If the input graph is undirected.
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See Also
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--------
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attracting_components
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number_attracting_components
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"""
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ac = list(attracting_components(G))
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if len(ac) == 1:
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return len(ac[0]) == len(G)
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return False
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