def detach(self, indices=None):
if indices is None:
segments = [list(range(len(self)))]
return Structures(self.points, segments, self.adjacency)
else:
points = self.points[indices]
adjacency = subgraph(self.adjacency, indices)
clockwise = find_clockwise(points, adjacency)
segments = [clockwise_traversal((0, 1), adjacency, clockwise)]
return Structures(points, segments, adjacency)
def check_isomorphism(adjacency, clockwise, other_adjacency):
"""Returns True if two plane graphs rooted graphs are isomorphs else False"""
for i in adjacency[0]:
edge = (0, i)
traversal = clockwise_traversal(edge, adjacency, clockwise)
permuted_adjacency = subgraph(adjacency, traversal)
if permuted_adjacency == other_adjacency:
return True
return False
def select_segments(indices, points, segments, adjacency=None):
if adjacency is not None:
adjacency = subgraph(adjacency, sorted(in_groups(segments)))
segments = [segments[i] for i in indices]
points = points[sorted(in_groups(segments))]
segments = relabel_groups(segments)
if adjacency is None:
return points, segments
else:
return points, segments, adjacency
def subgraph_isomorphism(adjacency, clockwise, subgraph_adjacency):
# TODO : Implement in Cython
"""Returns all clockwise ordered subgraph isomorphs.
Parameters:
----------
adjacency : list of sets
Adjacency list of larger graph, ordered according to a clockwise traversal
clockwise : dict
Dictionary directed edges as keys mapping to the next adjacent edge in the clockwise direction.
subgraph_adjacency : list of sets
Adjacency list of smaller graph, ordered according to a clockwise traversal
"""
outer_queue = []
for i in adjacency[0]:
outer_queue.append(Traversal([(0, i)], [], set()))
subgraph_order = len(subgraph_adjacency)
subgraph_adjacents = [subgraph_adjacency[n] - set(range(n)) for n in range(subgraph_order)]
degree = [len(adjacent) for adjacent in adjacency]
results = []
while outer_queue:
traversal = outer_queue.pop(0)
n = len(traversal)
if n == subgraph_order:
print(traversal.order,subgraph(adjacency, traversal.order))
if subgraph(adjacency, traversal.order) == subgraph_adjacency:
results.append(traversal)
continue
elif len(traversal.edges) == 0:
continue
else:
edge = traversal.edges.pop(0)
if not edge[0] in traversal.marked:
for i in range(degree[edge[0]]):
edge = clockwise[edge]
if edge[1] not in traversal.marked:
traversal.edges.append((edge[1], edge[0]))
traversal.marked.add(edge[0])
traversal.order.append(edge[0])
adjacent = adjacency[edge[0]] - traversal.marked
discrepancy = len(adjacent) - len(subgraph_adjacents[n])
if discrepancy > 0:
if len(subgraph_adjacents[n]) == 0:
traversal.marked.update(adjacent)
outer_queue.append(traversal)
else:
for i, combination in enumerate(itertools.combinations(adjacent, discrepancy)):
#if i == 0:
# outer_queue.append(traversal)
#else:
outer_queue.append(traversal.copy())
outer_queue[-1].marked.update(set(combination))
elif discrepancy < 0:
#outer_queue.append(traversal)
pass # TODO : Is this OK?
else:
outer_queue.append(traversal)
else:
outer_queue.append(traversal)
print(results)
return [traversal.order for traversal in results]
def adjacency(self):
return subgraph(self.structures.adjacency, self.segment)
structures = lattice_traversal(a, b, max_depth=5)
points = structures.points
adjacency = structures.adjacency
clockwise = find_clockwise(points, adjacency)
i = 0
n = 20
selected = set((0, ))
while len(selected) < n:
i = random.sample(adjacency[i], 1)[0]
selected.add(i)
selected = list(selected)
subgraph_points = points[selected]
subgraph_adjacency = subgraph(adjacency, selected)
root = 0
edge = (root, random.sample(subgraph_adjacency[root], 1)[0])
subgraph_clockwise = find_clockwise(subgraph_points, subgraph_adjacency)
traversal = clockwise_traversal(edge, subgraph_adjacency, subgraph_clockwise)
subgraph_points = subgraph_points[traversal]
subgraph_adjacency = subgraph(subgraph_adjacency, traversal)
isomorphisms = subgraph_isomorphism(adjacency, clockwise, subgraph_adjacency)
if not show_plots:
assert len(isomorphisms) >= 4
quit()
structures = lattice_traversal(a, b, max_depth=3)
points = structures.points
adjacency = structures.adjacency
clockwise = find_clockwise(points, adjacency)
i = 0
n = 10
selected = set((0, ))
while len(selected) < n:
i = random.sample(adjacency[i], 1)[0]
selected.add(i)
selected = list(selected)
subgraph_points = points[selected]
subgraph_adjacency = subgraph(adjacency, selected)
root = 0
edge = (root, random.sample(subgraph_adjacency[root], 1)[0])
subgraph_clockwise = find_clockwise(subgraph_points, subgraph_adjacency)
traversal = clockwise_traversal(edge, subgraph_adjacency, subgraph_clockwise)
subgraph_points = subgraph_points[traversal]
subgraph_adjacency = subgraph(subgraph_adjacency, traversal)
# import matplotlib.pyplot as plt
# plt.plot(points[:,0],points[:,1],'o')
# plt.plot(subgraph_points[:,0],subgraph_points[:,1],'x')
# plt.show()