# algorithms.graph.bipartite_graph¶

## Module: `algorithms.graph.bipartite_graph`¶

Inheritance diagram for `nipy.algorithms.graph.bipartite_graph`:

This module implements the BipartiteGraph class, used to represent weighted bipartite graph: it contains two types of vertices, say ‘left’ and ‘right’; then edges can only exist between ‘left’ and ‘right’ vertices. For simplicity the vertices of either side are labeled [1..V] and [1..W] respectively.

Author: Bertrand Thirion, 2006–2011

## `BipartiteGraph`¶

class nipy.algorithms.graph.bipartite_graph.BipartiteGraph(V, W, edges=None, weights=None)

Bases: `object`

Bipartite graph class

A graph for which there are two types of nodes, such that edges can exist only between nodes of type 1 and type 2 (not within) fields of this class: V (int, > 0) the number of type 1 vertices W (int, > 0) the number of type 2 vertices E: (int) the number of edges edges: array of shape (self.E, 2) reprensenting pairwise neighbors weights, array of shape (self.E), +1/-1 for scending/descending links

__init__(V, W, edges=None, weights=None)

Constructor

Parameters:
V (int), the number of vertices of subset 1
W (int), the number of vertices of subset 2
edges=None: array of shape (self.E, 2)

the edge array of the graph

weights=None: array of shape (self.E)

the associated weights array

copy()

returns a copy of self

set_edges(edges)

Set edges to graph

sets self.edges=edges if
1. edges has a correct size

2. edges take values in [0..V-1]*[0..W-1]

Parameters:
edges: array of shape(self.E, 2): set of candidate edges
set_weights(weights)

Set weights weights to edges

Parameters:
weights, array of shape(self.V): edges weights
subgraph_left(valid, renumb=True)

Extraction of a subgraph

Parameters:
valid, boolean array of shape self.V
renumb, boolean: renumbering of the (left) edges
Returns:
GNone or `BipartiteGraph` instance

A new BipartiteGraph instance with only the left vertices that are True. If sum(valid)==0, None is returned

subgraph_right(valid, renumb=True)

Extraction of a subgraph

Parameters:
validbool array of shape self.V
renumbbool, optional

renumbering of the (right) edges

Returns:
GNone or `BipartiteGraph` instance.

A new BipartiteGraph instance with only the right vertices that are True. If sum(valid)==0, None is returned

## Functions¶

Instantiates a weighted graph from a square 2D array

Parameters:
x: 2D array instance, the input array
Returns:
wg: BipartiteGraph instance
nipy.algorithms.graph.bipartite_graph.bipartite_graph_from_coo_matrix(x)

Instantiates a weighted graph from a (sparse) coo_matrix

Parameters:
x: scipy.sparse.coo_matrix instance, the input matrix
Returns:
bg: BipartiteGraph instance
nipy.algorithms.graph.bipartite_graph.check_feature_matrices(X, Y)

checks whether the dimensions of X and Y are consistent

Parameters:
X, Y arrays of shape (n1, p) and (n2, p)
where p = common dimension of the features
nipy.algorithms.graph.bipartite_graph.cross_eps(X, Y, eps=1.0)

Return the eps-neighbours graph of from X to Y

Parameters:
X, Y arrays of shape (n1, p) and (n2, p)
where p = common dimension of the features
eps=1, float: the neighbourhood size considered
Returns:
the resulting bipartite graph instance

Notes

for the sake of speed it is advisable to give PCA-preprocessed matrices X and Y.

nipy.algorithms.graph.bipartite_graph.cross_knn(X, Y, k=1)

return the k-nearest-neighbours graph of from X to Y

Parameters:
X, Y arrays of shape (n1, p) and (n2, p)
where p = common dimension of the features
eps=1, float: the neighbourhood size considered
Returns:
BipartiteGraph instance

Notes

For the sake of speed it is advised to give PCA-transformed matrices X and Y.