Alignment module¶

wlalign.alignment.apply_alignment(graph: numpy.ndarray, alignment: numpy.ndarray) → numpy.ndarray[source]¶

Permute the nodes of a graph according to a specified alignment.

Parameters

graph –

np.ndarray
Graph that is being permuted.
alignment –

np.ndarray
n-by-2 array with one row per node in the graph. The node indexed by the first element of each row is mapped to the second element in each row

Returns

np.ndarray: The permuted graph.

wlalign.alignment.length_wl_signature(k: int, l: int) → int[source]¶

Returns the length of the WL signature corresponding to the width and depth parameters given as input.

Parameters

k –

int
Width of the breadth-first search.
l –

int
Depth of the breadth-first search.

Returns

int: Length of the WL align signature.

Raises

ValueError – if k <= 0.
ValueError – if l <= 0.

wlalign.alignment.permutation_from_alignment(alignment: numpy.ndarray) → numpy.ndarray[source]¶

Transform a matching into a permutation matrix.

Parameters

alignment –

np.ndarray: n-by-2 array with one row per node in the graph. The node indexed by the first element of each row is mapped to the second element in each row

Returns

np.ndarray: Permutation matrix corresponding to the alignment

wlalign.alignment.signature_wl(g: numpy.ndarray, k: int, l: int, node: int, volumes: Optional[list] = None) → numpy.ndarray[source]¶

Compute the WL-align signature of a node of a graph from its adjacency matrix.

Parameters

g –

np.ndarray
Adjacency matrix of the graph.
k –

int
Width parameter of the breadth-first search.
l –

int
Depth parameter of the breadth-first search
node –

int
Index of the node of which the signature must be computed.
volumes –

Optional[list]
List containing the volume of each node. If not passed, it’s computed on the fly from the adjacency matrix.

Returns

np.ndarray: Signature of the node.

References

Matteo Frigo, Emilio Cruciani, David Coudert, Rachid Deriche, Emanuele Natale, Samuel Deslauriers-Gauthier; Network alignment and similarity reveal atlas-based topological differences in structural connectomes. Network Neuroscience 2021; doi: https://doi.org/10.1162/netn_a_00199

wlalign.alignment.wl_align(g1: numpy.ndarray, g2: numpy.ndarray, k: int, l: int) → numpy.ndarray[source]¶

Compute the WL alignment between two graphs as in Frigo et al., 2021.

Parameters

g1 –

np.ndarray
Adjacency matrix of the first graph to align.
g2 –

np.ndarray
Adjacency matrix of the second graph to align.
k –

int
Width parameter of the breadth-first search.
l –

int
Depth parameter of the breadth-first search

Returns

np.ndarray: Matrix with two columns and one row per node. The first element of each row is the index of the node in the first graph that is aligned with the node in the second graph indexed by the second element of the row.

References

Matteo Frigo, Emilio Cruciani, David Coudert, Rachid Deriche, Emanuele Natale, Samuel Deslauriers-Gauthier; Network alignment and similarity reveal atlas-based topological differences in structural connectomes. Network Neuroscience 2021; doi: https://doi.org/10.1162/netn_a_00199

Similarity module¶

wlalign.similarity.graph_jaccard_index(g1, g2)[source]¶

Compute the Graph Jaccard Index (GJI) between two graphs.

Parameters

g1 –

np.ndarray
Adjacency matrix of the first graph.
g2 –

np.ndarray
Adjacency matrix of the second graph.

Returns

float: Value of the GJI between the two graphs. The value will be in the [0, 1] range.

References

Matteo Frigo, Emilio Cruciani, David Coudert, Rachid Deriche, Emanuele Natale, Samuel Deslauriers-Gauthier; Network alignment and similarity reveal atlas-based topological differences in structural connectomes. Network Neuroscience 2021; doi: https://doi.org/10.1162/netn_a_00199

Utils module¶

wlalign.utils.check_can_write_file(fpath: str, force: bool = False) → None[source]¶

Check if a file can be written. The function checks if the file already exists, the user has the permission to write it, overwriting can be forced and, if the file does not exist, if the parent directory exists and is writable.

Parameters

fpath –

str
Path of the file to be checked.
force –

bool
True if the file can be overwritten, False otherwise.

Raises

FileExistsError – if the file exists and can not be overwritten.
PermissionError – if the file esists and the user does not have the permission to write it.
PermissionError – if the file does not exist, the parent directory exists and the user does not have the permission to write a file in it.
FileNotFoundError – if file does not exist and the parent directory does not exist.

wlalign.utils.check_compatible_adj(g1: numpy.ndarray, g2: numpy.ndarray)[source]¶

Check if two graphs have the same number of nodes.

Parameters

g1 –

np.ndarray
First graph to compare.
g2 –

np.ndarray
Second graph to compare.

Raises

ValueError – if the two adjacency matrices do not have the same number of rows and columns.

wlalign.utils.check_is_adj(g: numpy.ndarray)[source]¶

Check if a matrix is an adjacency matrix

Parameters

g –

np.ndarray: Matrix to be checked.

Raises

ValueError – if the matrix is not 2-dimensional.
ValueError – if the matrix is not square.

wlalign.utils.check_is_alignment(alignment: numpy.ndarray, n: Optional[int] = None)[source]¶

Check if a numpy array is a valid alignment.

Parameters

alignment –

np.ndarray
Alignment to be checked. Must be n-by-2 numpy array.
n –

Optional[int]
Number of nodes expected to be found in the alignment.

Raises

ValueError – if the alignment does not have 2 dimensions.
ValueError – if the alignment does not have 2 columns.
ValueError – if the alignment does not have n rows.
ValueError – if the alignment is not a 1-1 correspondence.

wlalign.utils.load_network(fpath: str, delimiter: str = ' ', skip: str = '#') → numpy.ndarray[source]¶

Load a network from a text file with the adjacency matrix

Parameters

fpath –

str
Path of the file where the adjacency matrix is saved.
delimiter –

str
Character that separates two consecutive entries in a row. Default: whitespace.
skip –

str
Lines that start with this character will be skipped.

Returns

np.ndarray: The adjacency matrix.

wlalign.utils.symmetrize_adj(g: numpy.ndarray) → numpy.ndarray[source]¶

Transform a graph from directed to undirected by summing the weights in the two directions of each edge.

Parameters

g –

np.ndarray: Adjacency matrix of the graph to symmetrize.

Returns

np.ndarray: Adjacency matrix of the symmetrized graph.