def _build_Gs(adj_mat):
"""
Build single-edge indicator matrix.
Build the sparse single-edge adjacency matrix `Gs` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Gs : sparse matrix
A single-edge adjacency matrix in sparse form.
"""
G = _build_G(adj_mat)
J = _build_J(adj_mat)
if sparse.issparse(adj_mat):
Gs = mcut._drop0_killdiag(G - G.multiply(J.T))
else:
Gs = mcut._drop0_killdiag(G - G * J.T)
return Gs
def _build_Js(adj_mat):
"""
Build single-edge indicator matrix.
Build the sparse single-edge indicator matrix `Js` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Js : sparse matrix
A single-edge indicator matrix in sparse form.
"""
Gs = _build_Gs(adj_mat)
if sparse.issparse(adj_mat):
Js = mcut._drop0_killdiag(Gs > 0)
else:
Js = mcut._drop0_killdiag(1 * (Gs > 0))
return Js
def _build_Gp(adj_mat):
"""
Build product matrix.
Build the sparse product matrix `Gp` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Gp : sparse matrix
A product matrix in sparse form.
"""
G = _build_G(adj_mat)
if sparse.issparse(adj_mat):
Gp = mcut._drop0_killdiag(G.multiply(G.T))
else:
Gp = mcut._drop0_killdiag(G * G.T)
return Gp
def _build_J(adj_mat):
"""
Build directed indicator matrix.
Build the sparse directed indicator matrix `J`
from a graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
J : sparse matrix
A directed indicator matrix in sparse form.
"""
G = _build_G(adj_mat)
if sparse.issparse(adj_mat):
J = mcut._drop0_killdiag(G > 0)
else:
J = mcut._drop0_killdiag(1 * (G > 0))
return J
def _build_Jn(adj_mat):
"""
Build vertex-distinct indicator matrix.
Build the vertex-distinct indicator matrix `Jn` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Jn : sparse matrix
A vertex-distinct indicator matrix.
"""
n = adj_mat.shape[0]
if sparse.issparse(adj_mat):
Jn = sparse.csr_matrix(mcut._drop0_killdiag(np.ones((n, n))))
else:
Jn = mcut._drop0_killdiag(np.ones((n, n)))
return Jn
def _build_J0(adj_mat):
"""
Build missing-edge indicator matrix.
Build the missing-edge indicator matrix `J0` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
J0 : sparse matrix
A missing-edge indicator matrix.
"""
G = _build_G(adj_mat)
if sparse.issparse(adj_mat):
J0 = sparse.csr_matrix(mcut._drop0_killdiag((G + G.T) == 0))
else:
J0 = mcut._drop0_killdiag((G + G.T) == 0)
return J0
def _build_Jd(adj_mat):
"""
Build double-edge indicator matrix.
Build the sparse double-edge indicator matrix `Jd` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Jd : sparse matrix
A double-edge indicator matrix in sparse form.
"""
Gd = _build_Gd(adj_mat)
if sparse.issparse(adj_mat):
Jd = mcut._drop0_killdiag(Gd > 0)
else:
Jd = mcut._drop0_killdiag(1 * (Gd > 0))
return Jd
def _build_Gd(adj_mat):
"""
Build double-edge adjacency matrix.
Build the sparse double-edge adjacency matrix `Gd` from a
graph adjacency matrix.
Parameters
----------
adj_mat : matrix
The original adjacency matrix.
Returns
-------
Gd : sparse matrix
A double-edge adjacency matrix in sparse form.
"""
J = _build_J(adj_mat)
G = _build_G(adj_mat)
if sparse.issparse(adj_mat):
Gd = mcut._drop0_killdiag((G + G.T).multiply(J).multiply(J.T))
else:
Gd = mcut._drop0_killdiag((G + G.T) * J * J.T)
return Gd
def test_drop0_kill_diag():
adj_mat_dense = np.array(range(-1, 8)).reshape((3, 3))
adj_mat_sparse = sparse.csr_matrix(adj_mat_dense)
ans = np.array([0, 0, 1, 2, 0, 4, 5, 6, 0]).reshape((3, 3))
assert np.allclose(mcut._drop0_killdiag(adj_mat_dense), ans)
assert np.allclose(mcut._drop0_killdiag(adj_mat_sparse).toarray(), ans)
def sample_dsbm(block_sizes,
connection_matrix,
weight_matrix=None,
sample_weight_type="unweighted"):
"""
Sample a directed stochastic block model (DSBM).
Sample the (weighted) adjacency matrix of a (weighted) directed stochastic
block model (DSBM) with specified parameters.
Parameters
----------
block_sizes : list of int
A list containing the size of each block of vertices.
connection_matrix : matrix
A matrix containing the block-to-block connection probabilities.
sample_weight_type : str
The type of weighting scheme.
One of `"unweighted"`, `"constant"` or `"poisson"`.
weight_matrix : matrix
A matrix containing the block-to-block weight
parameters.
Unused for `sample_weight_type = "constant"`.
Defaults to `None`.
Returns
-------
adj_mat : sparse matrix
A randomly sampled (weighted) adjacency matrix of a DSBM.
Examples
--------
>>> block_sizes = [10, 10]
>>> connection_matrix = np.array([0.8, 0.1, 0.1, 0.8]).reshape((2, 2))
>>> weight_matrix = np.array([10, 3, 3, 10]).reshape((2, 2))
>>> sample_dsbm(block_sizes, connection_matrix, weight_matrix, "poisson")
"""
# check args
assert block_sizes == [int(x) for x in block_sizes]
assert all(x > 0 for x in block_sizes)
assert len(block_sizes) == connection_matrix.shape[0]
assert len(block_sizes) == connection_matrix.shape[1]
assert (connection_matrix >= 0).all()
assert (connection_matrix <= 1).all()
assert sample_weight_type in ["unweighted", "constant", "poisson"]
if sample_weight_type != "unweighted":
assert weight_matrix is not None
assert len(block_sizes) == weight_matrix.shape[0]
assert len(block_sizes) == weight_matrix.shape[1]
assert (weight_matrix >= 0).all()
# initialize variables
k = len(block_sizes)
block_list = []
for i in range(k):
row_list = []
for j in range(k):
# block parameters
ni = block_sizes[i]
nj = block_sizes[j]
p = connection_matrix[i, j]
# generate block
if sample_weight_type == "unweighted":
w = 1
else:
w = weight_matrix[i, j]
block = mcut._random_sparse_matrix(ni, nj, p, sample_weight_type,
w)
row_list.append(block)
block_list.append(row_list)
# build from dense blocks
if isinstance(block_list[0][0], np.ndarray):
adj_mat = np.block(block_list)
# build from sparse blocks
else:
adj_mat = sparse.bmat(block_list)
adj_mat = sparse.csr_matrix(adj_mat)
adj_mat = mcut._drop0_killdiag(adj_mat)
return adj_mat