def is_independent_set(G, nodes):
"""Return whether or not the *nodes* comprises an independent set.
An set *S* of nodes in *G* is called an *independent set* if no two
nodes in S are neighbors of one another.
Parameters
----------
G : NetworkX graph
An undirected graph.
nodes : list, set
An iterable container of nodes in G. Only nodes existing in G
will be considered. Any other nodes will be ignored.
Returns
-------
bool
True if the the nodes in *nodes* comprise an independent set,
False otherwise.
See Also
--------
is_k_independent_set
"""
S = set(n for n in nodes if n in G)
return set(set_neighborhood(G, S)).intersection(S) == set()
def is_total_dominating_set(G, nodes):
"""Return whether or not nodes comprises a total dominating set.
A * total dominating set* is a set of nodes with the property that
every node in the graph is adjacent to some node in the set.
Parameters
----------
G : NetworkX graph
An undirected graph.
nodes : list, set
An iterable container of nodes in G.
Returns
-------
boolean
True if the nodes in nbunch comprise a k-dominating set, and
False otherwise.
"""
# exclude any nodes that aren't in G
S = set(n for n in nodes if n in G)
return set(set_neighborhood(G, S)) == set(G.nodes())