# -*- coding: utf-8 -*- # Copyright (C) 2004-2017 by # Aric Hagberg # Dan Schult # Pieter Swart # All rights reserved. # BSD license. # # Authors: Christopher Ellison """Attracting components.""" import networkx as nx from networkx.utils.decorators import not_implemented_for __all__ = ['number_attracting_components', 'attracting_components', 'is_attracting_component', 'attracting_component_subgraphs', ] @not_implemented_for('undirected') 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 sets A generator of sets of nodes, one for each attracting component of G. Raises ------ NetworkXNotImplemented : If the input graph is undirected. 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') 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. Raises ------ NetworkXNotImplemented : If the input graph is undirected. See Also -------- attracting_components is_attracting_component attracting_component_subgraphs """ n = len(list(attracting_components(G))) return n @not_implemented_for('undirected') 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. Raises ------ NetworkXNotImplemented : If the input graph is undirected. 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') 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. Raises ------ NetworkXNotImplemented : If the input graph is undirected. 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)