dgl.DGLGraph.inc

DGLGraph.inc(typestr, ctx=device(type='cpu'), etype=None)[source]

Return the incidence matrix representation of edges with the given edge type.

An incidence matrix is an n-by-m sparse matrix, where n is the number of nodes and m is the number of edges. Each nnz value indicating whether the edge is incident to the node or not.

There are three types of incidence matrices \(I\):

in:
- \(I[v, e] = 1\) if \(e\) is the in-edge of \(v\) (or \(v\) is the dst node of \(e\));
- \(I[v, e] = 0\) otherwise.
out:
- \(I[v, e] = 1\) if \(e\) is the out-edge of \(v\) (or \(v\) is the src node of \(e\));
- \(I[v, e] = 0\) otherwise.
both (only if source and destination node type are the same):
- \(I[v, e] = 1\) if \(e\) is the in-edge of \(v\);
- \(I[v, e] = -1\) if \(e\) is the out-edge of \(v\);
- \(I[v, e] = 0\) otherwise (including self-loop).

Parameters:

typestr (str) – Can be either in, out or both
ctx (context, optional) – The context of returned incidence matrix. (Default: cpu)
etype (str or (str, str, str), optional) –
The type names of the edges. The allowed type name formats are:
- (str, str, str) for source node type, edge type and destination node type.
- or one str edge type name if the name can uniquely identify a triplet format in the graph.
Can be omitted if the graph has only one type of edges.

Returns:

The incidence matrix.

Return type:

Framework SparseTensor

Examples

The following example uses PyTorch backend.

>>> import dgl

>>> g = dgl.graph(([0, 1], [0, 2]))
>>> g.inc('in')
tensor(indices=tensor([[0, 2],
                       [0, 1]]),
       values=tensor([1., 1.]),
       size=(3, 2), nnz=2, layout=torch.sparse_coo)
>>> g.inc('out')
tensor(indices=tensor([[0, 1],
                       [0, 1]]),
       values=tensor([1., 1.]),
       size=(3, 2), nnz=2, layout=torch.sparse_coo)
>>> g.inc('both')
tensor(indices=tensor([[1, 2],
                       [1, 1]]),
       values=tensor([-1.,  1.]),
       size=(3, 2), nnz=2, layout=torch.sparse_coo)