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This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.algorithms.components.attracting

# -*- coding: utf-8 -*-
"""
Attracting components.
"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
import networkx as nx
from networkx.utils.decorators import not_implemented_for
__authors__ = "\n".join(['Christopher Ellison'])
__all__ = ['number_attracting_components',
'attracting_components',
'is_attracting_component',
'attracting_component_subgraphs',
]

@not_implemented_for('undirected')
[docs]def attracting_components(G): """Generates 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 : generator of 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 = list(nx.strongly_connected_components(G)) cG = nx.condensation(G, scc) for n in cG: if cG.out_degree(n) == 0: yield scc[n]
@not_implemented_for('undirected')
[docs]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(list(attracting_components(G))) return n
@not_implemented_for('undirected')
[docs]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 = list(attracting_components(G)) if len(ac[0]) == len(G): attracting = True else: attracting = False return attracting
@not_implemented_for('undirected')
[docs]def attracting_component_subgraphs(G, copy=True): """Generates 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. copy : bool If copy is True, graph, node, and edge attributes are copied to the subgraphs. See Also -------- attracting_components number_attracting_components is_attracting_component """ for ac in attracting_components(G): if copy: yield G.subgraph(ac).copy() else: yield G.subgraph(ac)