# -*- coding: utf-8 -*- # Copyright (C) 2004-2019 by # Aric Hagberg # Dan Schult # Pieter Swart # All rights reserved. # BSD license. # # Authors: Eben Kenah # Aric Hagberg (hagberg@lanl.gov) # Christopher Ellison """Connected components.""" import warnings as _warnings import networkx as nx from networkx.utils.decorators import not_implemented_for from ...utils import arbitrary_element __all__ = [ 'number_connected_components', 'connected_components', 'is_connected', 'node_connected_component', ] @not_implemented_for('directed') def connected_components(G): """Generate connected components. Parameters ---------- G : NetworkX graph An undirected graph Returns ------- comp : generator of sets A generator of sets of nodes, one for each component of G. Raises ------ NetworkXNotImplemented: If G is directed. Examples -------- Generate a sorted list of connected components, largest first. >>> G = nx.path_graph(4) >>> nx.add_path(G, [10, 11, 12]) >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)] [4, 3] If you only want the largest connected component, it's more efficient to use max instead of sort. >>> largest_cc = max(nx.connected_components(G), key=len) To create the induced subgraph of each component use: >>> S = [G.subgraph(c).copy() for c in connected_components(G)] See Also -------- strongly_connected_components weakly_connected_components Notes ----- For undirected graphs only. """ seen = set() for v in G: if v not in seen: c = set(_plain_bfs(G, v)) yield c seen.update(c) def number_connected_components(G): """Returns the number of connected components. Parameters ---------- G : NetworkX graph An undirected graph. Returns ------- n : integer Number of connected components See Also -------- connected_components number_weakly_connected_components number_strongly_connected_components Notes ----- For undirected graphs only. """ return sum(1 for cc in connected_components(G)) @not_implemented_for('directed') def is_connected(G): """Returns True if the graph is connected, False otherwise. Parameters ---------- G : NetworkX Graph An undirected graph. Returns ------- connected : bool True if the graph is connected, false otherwise. Raises ------ NetworkXNotImplemented: If G is directed. Examples -------- >>> G = nx.path_graph(4) >>> print(nx.is_connected(G)) True See Also -------- is_strongly_connected is_weakly_connected is_semiconnected is_biconnected connected_components Notes ----- For undirected graphs only. """ if len(G) == 0: raise nx.NetworkXPointlessConcept('Connectivity is undefined ', 'for the null graph.') return sum(1 for node in _plain_bfs(G, arbitrary_element(G))) == len(G) @not_implemented_for('directed') def node_connected_component(G, n): """Returns the set of nodes in the component of graph containing node n. Parameters ---------- G : NetworkX Graph An undirected graph. n : node label A node in G Returns ------- comp : set A set of nodes in the component of G containing node n. Raises ------ NetworkXNotImplemented: If G is directed. See Also -------- connected_components Notes ----- For undirected graphs only. """ return set(_plain_bfs(G, n)) def _plain_bfs(G, source): """A fast BFS node generator""" G_adj = G.adj seen = set() nextlevel = {source} while nextlevel: thislevel = nextlevel nextlevel = set() for v in thislevel: if v not in seen: yield v seen.add(v) nextlevel.update(G_adj[v])