def SimulateSbm(sbm_data,
num_vertices,
num_edges,
pi,
prop_mat,
out_degs=None,
pi2=None):
"""Generates a stochastic block model, storing data in sbm_data.graph.
This function uses graph_tool.generate_sbm. Refer to that
documentation for more information on the model and parameters.
This function can generate a heterogeneous SBM graph, meaning each node is
exactly one of two types (and both types are present). To generate a
heteroteneous SBM graph, `pi2` must be supplied, and additional fields of
`sbm_data` will be filled. See the StochasticBlockModel dataclass for details.
Args:
sbm_data: StochasticBlockModel dataclass to store result data.
num_vertices: (int) number of nodes in the graph.
num_edges: (float) expected number of edges in the graph.
pi: iterable of non-zero community size relative proportions. Community i
will be pi[i] / pi[j] times larger than community j.
prop_mat: square, symmetric matrix of community edge count rates.
out_degs: Out-degree propensity for each node. If not provided, a constant
value will be used. Note that the values will be normalized inside each
group, if they are not already so.
pi2: This is the pi vector for the vertices of type 2. Type 2 community k
will be pi2[k] / pi[j] times larger than type 1 community j. Supplying
this argument produces a heterogeneous model.
Returns: (none)
"""
if pi2 is None: pi2 = []
k1, k2 = len(pi), len(pi2)
pi = np.array(list(pi) + list(pi2)).astype(np.float64)
pi /= np.sum(pi)
if prop_mat.shape[0] != len(pi) or prop_mat.shape[1] != len(pi):
raise ValueError("prop_mat must be k x k; k = len(pi1) + len(pi2)")
sbm_data.graph_memberships = _GenerateNodeMemberships(num_vertices, pi)
sbm_data.type1_clusters = sorted(list(set(sbm_data.graph_memberships)))
if len(pi2) > 0:
sbm_data.cross_links = hsu.GetCrossLinks([k1, k2], 0, 1)
type1_clusters, type2_clusters = zip(*sbm_data.cross_links)
sbm_data.type1_clusters = sorted(list(set(type1_clusters)))
sbm_data.type2_clusters = sorted(list(set(type2_clusters)))
edge_counts = _ComputeExpectedEdgeCounts(num_edges, num_vertices, pi,
prop_mat)
sbm_data.graph = generation.generate_sbm(sbm_data.graph_memberships,
edge_counts, out_degs)
graph_tool.stats.remove_self_loops(sbm_data.graph)
graph_tool.stats.remove_parallel_edges(sbm_data.graph)
sbm_data.graph.reindex_edges()
def SimulateSbm(sbm_data,
num_vertices,
num_edges,
pi,
prop_mat,
out_degs=None,
num_vertices2=0,
pi2=None):
"""Generates a stochastic block model, storing data in sbm_data.graph.
This function uses graph_tool.generate_sbm. Refer to that
documentation for more information on the model and parameters.
This function can generate a heterogeneous SBM graph, meaning each node is
exactly one of two types (and both types are present). To generate a
heteroteneous SBM graph, both `num_vertices2` and `pi2` must be non-zero and
supplied (respectively). When this happens, additional fields of `sbm_data`
are filled. See the StochasticBlockModel dataclass for full details.
Args:
sbm_data: StochasticBlockModel dataclass to store result data.
num_vertices: (int) number of nodes in the graph.
num_edges: (int) expected number of edges in the graph.
pi: iterable of non-zero community size proportions. Must sum to 1.0.
prop_mat: square, symmetric matrix of community edge count rates.
out_degs: Out-degree propensity for each node. If not provided, a constant
value will be used. Note that the values will be normalized inside each
group, if they are not already so.
num_vertices2: If simulating a heterogeneous SBM, this is the number of
vertices of type 2.
pi2: If simulating a heterogeneous SBM, this is the pi vector for the
vertices of type 2. Must sum to 1.0.
Returns: (none)
"""
if ((num_vertices2 == 0 and pi2 is not None)
or (num_vertices2 > 0 and pi2 is None)):
raise ValueError(
"num_vertices2 and pi2 must be either both supplied or both None")
if num_vertices2 == 0:
pi2 = []
# Equivalent to assertAlmostEqual(np.sum(pi), 1.0, places=12)
# https://docs.python.org/3/library/unittest.html#unittest.TestCase.assertNotAlmostEqual
#
# Some leniency is required here because some theoretically-valid ways to
# programmatically compute a simplex vector suffer from precision errors. One
# example of this is in the simulate_sbm_community_sizes_seven_groups test
# from sbm_simulator_test.py. Places>=12 covers known similar cases (to date).
if round(abs(np.sum(pi) - 1.0), 12) != 0:
raise ValueError("entries of pi ( must sum to 1.0")
if len(pi2) > 0 and round(abs(np.sum(pi2) - 1.0), 12) != 0:
raise ValueError("entries of pi2 ( must sum to 1.0")
k1, k2 = len(pi), len(pi2)
pi = np.array(list(pi) + list(pi2))
pi /= np.sum(pi)
if prop_mat.shape[0] != len(pi) or prop_mat.shape[1] != len(pi):
raise ValueError("prop_mat must be k x k; k = len(pi1) + len(pi2)")
sbm_data.graph_memberships = _GenerateNodeMemberships(
num_vertices + num_vertices2, pi)
sbm_data.type1_clusters = sorted(list(set(sbm_data.graph_memberships)))
if num_vertices2 > 0:
sbm_data.cross_links = hsu.GetCrossLinks(k1, k2)
type1_clusters, type2_clusters = zip(*sbm_data.cross_links)
sbm_data.type1_clusters = sorted(list(set(type1_clusters)))
sbm_data.type2_clusters = sorted(list(set(type2_clusters)))
edge_counts = _ComputeExpectedEdgeCounts(num_edges,
num_vertices + num_vertices2, pi,
prop_mat)
sbm_data.graph = generation.generate_sbm(sbm_data.graph_memberships,
edge_counts, out_degs)
graph_tool.stats.remove_self_loops(sbm_data.graph)
graph_tool.stats.remove_parallel_edges(sbm_data.graph)
sbm_data.graph.reindex_edges()
def test_three_type_mixed12(self):
self.assertEqual(hsu.GetCrossLinks([3, 4, 2], 0, 1), [(0, 4), (0, 6),
(2, 4), (2, 6),
(1, 3), (1, 5)])
def test_second_greater_than_first(self):
self.assertEqual(hsu.GetCrossLinks([2, 3], 0, 1), [(0, 2), (0, 4),
(1, 3)])
def test_first_greater_than_second(self):
self.assertEqual(hsu.GetCrossLinks([3, 2], 0, 1), [(0, 4), (2, 4),
(1, 3)])
def test_equal_sizes(self):
self.assertEqual(hsu.GetCrossLinks([2, 2], 0, 1), [(0, 2), (1, 3)])
def test_first_greater_than_second(self):
self.assertEqual(hsu.GetCrossLinks(2, 1), [(0, 2), (1, 2)])