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Source code for networkx.algorithms.dominating
# -*- coding: utf-8 -*- import networkx as nx __author__ = '\n'.join(['Jordi Torrents <email@example.com>']) __all__ = [ 'dominating_set', 'is_dominating_set'][docs]def dominating_set(G, start_with=None): r"""Finds a dominating set for the graph G. A dominating set for a graph `G = (V, E)` is a node subset `D` of `V` such that every node not in `D` is adjacent to at least one member of `D` _. Parameters ---------- G : NetworkX graph start_with : Node (default=None) Node to use as a starting point for the algorithm. Returns ------- D : set A dominating set for G. Notes ----- This function is an implementation of algorithm 7 in _ which finds some dominating set, not necessarily the smallest one. See also -------- is_dominating_set References ---------- ..  http://en.wikipedia.org/wiki/Dominating_set ..  Abdol-Hossein Esfahanian. Connectivity Algorithms. http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf """ all_nodes = set(G) if start_with is None: v = set(G).pop() # pick a node else: if start_with not in G: raise nx.NetworkXError('node %s not in G' % start_with) v = start_with D = set([v]) ND = set(G[v]) other = all_nodes - ND - D while other: w = other.pop() D.add(w) ND.update([nbr for nbr in G[w] if nbr not in D]) other = all_nodes - ND - D return D[docs]def is_dominating_set(G, nbunch): r"""Checks if nodes in nbunch are a dominating set for G. A dominating set for a graph `G = (V, E)` is a node subset `D` of `V` such that every node not in `D` is adjacent to at least one member of `D` _. Parameters ---------- G : NetworkX graph nbunch : Node container See also -------- dominating_set References ---------- ..  http://en.wikipedia.org/wiki/Dominating_set """ testset = set(n for n in nbunch if n in G) nbrs = set() for n in testset: nbrs.update(G[n]) if len(set(G) - testset - nbrs) > 0: return False else: return True