"""
Utility functions for graph-related operations with sparse adjacency matrices
(scipy.sparse.csr_matrix) using and supplementing scipy's
[compressed sparse graph routines](
https://docs.scipy.org/doc/scipy/reference/sparse.csgraph.html).
"""
from scipy.sparse import csgraph as csg
from scipy.sparse import csr_matrix
import numpy as np
def is_connected(adj):
"""
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix.
Returns
-------
connected : `bool`
`True` if graph defined by adjecency matrix `adj` is connected.
`False` otherwise.
Examples
--------
>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> connected = csr_matrix(np.array([[0, 1],
... [1, 0]]))
>>> is_connected(connected)
True
>>> disconnected = csr_matrix(np.array([[0, 0],
... [0, 0]]))
>>> is_connected(disconnected)
False
"""
n_connected_components = csg.connected_components(adj, directed=False,
return_labels=False)
return True if n_connected_components == 1 else False
def neighbors(adj, area):
"""
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix.
area : int
An area specified as index in the graph represented by the adjacency
matrix `adj`. The integer must be in `{0, 1, ..., adj.shape[0]-1}`.
Returns
-------
neighs : :class:`numpy.ndarray`
The neighbors of `area`.
Examples
--------
>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> adjacency_matrix = csr_matrix(np.array([[0, 1, 1],
... [1, 0, 0],
... [1, 0, 0]]))
>>> (neighbors(adjacency_matrix, 0) == np.array([1, 2])).all()
True
>>> (neighbors(adjacency_matrix, 1) == np.array([0])).all()
True
"""
return adj[area].nonzero()[1]
def sub_adj_matrix(adj, nodes, wo_nodes=None):
"""
Parameters
----------
adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix.
nodes : :class:`numpy.ndarray`
1-dimensional array of nodes in the graph represented by the `adj`
argument. The elements in `nodes` are (distinct) integers in
`{0, 1, ..., nodes.shape[0]}`.
wo_nodes : slice, int, array of ints, or None
Nodes to neglect from the `nodes` argument.
Returns
-------
sub_adj : :class:`scipy.sparse.csr_matrix`
Adjacency matrix of the subgraph consisting of only the nodes in the
`nodes` argument.
Examples
--------
>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> adjacency_matrix = csr_matrix(np.array([[0, 1, 1],
... [1, 0, 0],
... [1, 0, 0]]))
>>> nodes = np.array([0, 2])
>>> obtained = sub_adj_matrix(adjacency_matrix, nodes)
>>> desired = np.array([[0, 1],
... [1, 0]])
>>> (obtained.todense() == desired).all()
True
>>> nodes = np.array([1, 2])
>>> obtained = sub_adj_matrix(adjacency_matrix, nodes)
>>> desired = np.array([[0, 0],
... [0, 0]])
>>> (obtained.todense() == desired).all()
True
>>> type(obtained) == csr_matrix
True
>>> # tests for `wo_nodes` argument
>>> all_nodes = np.arange(adjacency_matrix.shape[0])
>>> neglected_nodes = np.array([1])
>>> obtained = sub_adj_matrix(adjacency_matrix, all_nodes, neglected_nodes)
>>> desired = np.array([[0, 1],
... [1, 0]])
>>> (obtained.todense() == desired).all()
True
"""
if wo_nodes is not None:
mask = np.in1d(nodes, wo_nodes, invert=True)
nodes = nodes[mask]
nodes = nodes[:, None]
return csr_matrix(adj[nodes, nodes.T])
