def bron_kerbosch(self, P: Set[Node], R: Set[Node], X: Set[Node],
Cs: List[Set[Node]]):
"""!
\brief apply bron kerbosch algorithm for finding maximal cliques
Code taken from: arxiv.org/1006.5440
\code
proc BronKerbosch(P,R,X)
1: if P∪X = empty then
2: report R as a maximal clique
3: end if
4: for each vertex v∈P do
5: BronKerbosch(P ∩ Neigbours(v), R ∪ {v}, X ∩ Neighbours(v))
6: P←P\{v}
7: X←X∪{v}
8: end for
\endcode
"""
if len(P.union(X)) == 0:
Cs.append(R)
for v in P:
self.bron_kerbosch(
P=P.intersection(BaseGraphOps.neighbours_of(self, v)),
R=R.union([v]),
X=X.intersection(BaseGraphOps.neighbours_of(self, v)),
Cs=Cs,
)
P = P.difference([v])
X = X.union([v])
def markov_blanket(self, t: NumCatRVariable) -> Set[NumCatRVariable]:
"""!
get markov blanket of a node from K. Murphy, 2012, p. 662
"""
if BaseGraphOps.is_in(self, t) is False:
raise ValueError("Node not in graph: " + str(t))
ns: Set[NumCatRVariable] = BaseGraphOps.neighbours_of(self, t)
return ns
def order_by_greedy_metric(
self,
nodes: Set[NumCatRVariable],
s: Callable[[Graph, Dict[Node, bool]],
Optional[Node]] = min_unmarked_neighbours,
) -> Dict[str, int]:
"""!
From Koller and Friedman 2009, p. 314
"""
marked = {n.id(): False for n in nodes}
cardinality = {n.id(): -1 for n in nodes}
for i in range(len(nodes)):
X = s(g=self, nodes=nodes, marked=marked)
if X is not None:
cardinality[X.id()] = i
TEMP = BaseGraphOps.neighbours_of(self, X)
while TEMP:
n_x = TEMP.pop()
for n in BaseGraphOps.neighbours_of(self, X):
self = BaseGraphAlgOps.added_edge_between_if_none(
self, n_x, n, is_directed=False)
marked[X.id()] = True
return cardinality
def nb_neighbours_of(g: AbstractGraph, n: AbstractNode) -> int:
"""!
\brief obtain number of neighbours of a given node.
\param n node whose neighbour set we are interested in.
\see Graph.neighbours_of
Number of nodes in the neighbour set of n.
\code{.py}
>>> n1 = Node("n1", {})
>>> n2 = Node("n2", {})
>>> n3 = Node("n3", {})
>>> n4 = Node("n4", {})
>>> e1 = Edge(
>>> "e1", start_node=n1, end_node=n2, edge_type=EdgeType.UNDIRECTED
>>> )
>>> e2 = Edge(
>>> "e2", start_node=n2, end_node=n3, edge_type=EdgeType.UNDIRECTED
>>> )
>>> e3 = Edge(
>>> "e3", start_node=n3, end_node=n4, edge_type=EdgeType.UNDIRECTED
>>> )
>>> graph_2 = Graph(
>>> "g2",
>>> data={"my": "graph", "data": "is", "very": "awesome"},
>>> nodes=set([n1, n2, n3, n4]),
>>> edges=set([e1, e2, e3]),
>>> )
>>> graph_2.nb_neighbours_of(n2)
>>> 2
\endcode
"""
return len(BaseGraphOps.neighbours_of(g, n))
def test_neighbours_of(self):
ndes = set(
[n.id() for n in BaseGraphOps.neighbours_of(self.graph_2, self.n2)]
)
self.assertEqual(ndes, set([self.n1.id(), self.n3.id()]))