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+# -*- coding: utf-8 -*-
+"""
+Attracting components.
+"""
+# Copyright (C) 2004-2011 by
+# Aric Hagberg <hagberg@lanl.gov>
+# Dan Schult <dschult@colgate.edu>
+# Pieter Swart <swart@lanl.gov>
+# All rights reserved.
+# BSD license.
+import networkx as nx
+__authors__ = "\n".join(['Christopher Ellison'])
+__all__ = ['number_attracting_components',
+ 'attracting_components',
+ 'is_attracting_component',
+ 'attracting_component_subgraphs',
+ ]
+
+def attracting_components(G):
+ """Returns a list of attracting components in `G`.
+
+ An attracting component in a directed graph `G` is a strongly connected
+ component with the property that a random walker on the graph will never
+ leave the component, once it enters the component.
+
+ The nodes in attracting components can also be thought of as recurrent
+ nodes. If a random walker enters the attractor containing the node, then
+ the node will be visited infinitely often.
+
+ Parameters
+ ----------
+ G : DiGraph, MultiDiGraph
+ The graph to be analyzed.
+
+ Returns
+ -------
+ attractors : list
+ The list of attracting components, sorted from largest attracting
+ component to smallest attracting component.
+
+ See Also
+ --------
+ number_attracting_components
+ is_attracting_component
+ attracting_component_subgraphs
+
+ """
+ scc = nx.strongly_connected_components(G)
+ cG = nx.condensation(G, scc)
+ attractors = [scc[n] for n in cG if cG.out_degree(n) == 0]
+ attractors.sort(key=len,reverse=True)
+ return attractors
+
+
+def number_attracting_components(G):
+ """Returns the number of attracting components in `G`.
+
+ Parameters
+ ----------
+ G : DiGraph, MultiDiGraph
+ The graph to be analyzed.
+
+ Returns
+ -------
+ n : int
+ The number of attracting components in G.
+
+ See Also
+ --------
+ attracting_components
+ is_attracting_component
+ attracting_component_subgraphs
+
+ """
+ n = len(attracting_components(G))
+ return n
+
+
+def is_attracting_component(G):
+ """Returns True if `G` consists of a single attracting component.
+
+ Parameters
+ ----------
+ G : DiGraph, MultiDiGraph
+ The graph to be analyzed.
+
+ Returns
+ -------
+ attracting : bool
+ True if `G` has a single attracting component. Otherwise, False.
+
+ See Also
+ --------
+ attracting_components
+ number_attracting_components
+ attracting_component_subgraphs
+
+ """
+ ac = attracting_components(G)
+ if len(ac[0]) == len(G):
+ attracting = True
+ else:
+ attracting = False
+ return attracting
+
+
+def attracting_component_subgraphs(G):
+ """Returns a list of attracting component subgraphs from `G`.
+
+ Parameters
+ ----------
+ G : DiGraph, MultiDiGraph
+ The graph to be analyzed.
+
+ Returns
+ -------
+ subgraphs : list
+ A list of node-induced subgraphs of the attracting components of `G`.
+
+ Notes
+ -----
+ Graph, node, and edge attributes are copied to the subgraphs.
+
+ See Also
+ --------
+ attracting_components
+ number_attracting_components
+ is_attracting_component
+
+ """
+ subgraphs = [G.subgraph(ac).copy() for ac in attracting_components(G)]
+ return subgraphs
+