def test_degeneracy_ordering_nonempty(adjacencies: List[Set[Vertex]]) -> None:
g = UndirectedGraph(adjacencies=adjacencies)
connected_vertices = g.connected_vertices()
ordering = list(degeneracy_ordering(g))
assert set(ordering) == connected_vertices
assert all(g.degree(ordering[0]) <= g.degree(v) for v in ordering[1:])
ordering_min1 = list(degeneracy_ordering(g, drop=1))
assert ordering_min1 == ordering[:-1]
def degeneracy_ordering(graph: UndirectedGraph,
drop: int = 0) -> Generator[Vertex, None, None]:
"""
Iterate connected vertices, lowest degree first.
drop=N: omit last N vertices
"""
assert drop >= 0
priority_per_node = [-2] * graph.order
max_degree = 0
num_candidates = 0
for c in range(graph.order):
if degree := graph.degree(c):
priority_per_node[c] = degree
max_degree = max(max_degree, degree)
num_candidates += 1
def visit(graph: UndirectedGraph, reporter: Reporter, pivot_choice_X: bool,
candidates: Set[Vertex], excluded: Set[Vertex],
clique: List[Vertex]) -> None:
assert all(graph.degree(v) > 0 for v in candidates)
assert all(graph.degree(v) > 0 for v in excluded)
assert candidates.isdisjoint(excluded)
assert len(candidates) >= 1
if len(candidates) == 1:
# Same logic as below, stripped down for this common case
for v in candidates:
neighbours = graph.adjacencies[v]
assert neighbours
if excluded.isdisjoint(neighbours):
reporter.record(clique + [v])
return
# Quickly handle locally unconnected candidates while finding pivot
remaining_candidates = []
seen_local_degree = 0
for v in candidates:
neighbours = graph.adjacencies[v]
local_degree = len(candidates.intersection(neighbours))
if local_degree == 0:
# Same logic as below, stripped down
if neighbours.isdisjoint(excluded):
reporter.record(clique + [v])
else:
if seen_local_degree < local_degree:
seen_local_degree = local_degree
pivot = v
remaining_candidates.append(v)
if seen_local_degree == 0:
return
if pivot_choice_X:
for v in excluded:
neighbours = graph.adjacencies[v]
local_degree = len(candidates.intersection(neighbours))
if seen_local_degree < local_degree:
seen_local_degree = local_degree
pivot = v
for v in remaining_candidates:
neighbours = graph.adjacencies[v]
assert neighbours
if pivot not in neighbours:
candidates.remove(v)
if neighbouring_candidates := candidates.intersection(neighbours):
neighbouring_excluded = excluded.intersection(neighbours)
visit(graph=graph,
reporter=reporter,
pivot_choice_X=pivot_choice_X,
candidates=neighbouring_candidates,
excluded=neighbouring_excluded,
clique=clique + [v])
elif excluded.isdisjoint(neighbours):
reporter.record(clique + [v])
excluded.add(v)
def visit(graph: UndirectedGraph, reporter: Reporter, candidates: Set[Vertex],
excluded: Set[Vertex], clique: List[Vertex]) -> None:
assert all(graph.degree(v) > 0 for v in candidates)
assert all(graph.degree(v) > 0 for v in excluded)
assert candidates.isdisjoint(excluded)
assert candidates
while candidates:
v = candidates.pop()
neighbours = graph.adjacencies[v]
neighbouring_candidates = candidates.intersection(neighbours)
if neighbouring_candidates:
neighbouring_excluded = excluded.intersection(neighbours)
visit(graph,
reporter,
candidates=neighbouring_candidates,
excluded=neighbouring_excluded,
clique=clique + [v])
elif excluded.isdisjoint(neighbours):
reporter.record(clique + [v])
excluded.add(v)
