region.csgraph_utils module

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).

region.csgraph_utils.is_connected(adj)

Parameters:adj (scipy.sparse.csr_matrix) – Adjacency matrix. Returns:connected – True if graph defined by adjecency matrix adj is connected. False otherwise. Return type:bool

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

region.csgraph_utils.neighbors(adj, area)

Parameters:

• adj (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 – The neighbors of area.

Return type:

numpy.ndarray

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

region.csgraph_utils.sub_adj_matrix(adj, nodes, wo_nodes=None)

Parameters:

• adj (scipy.sparse.csr_matrix) – Adjacency matrix.
• nodes (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 – Adjacency matrix of the subgraph consisting of only the nodes in the nodes argument.

Return type:

scipy.sparse.csr_matrix

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