mindspore_gl.graph.norm

mindspore_gl.graph.norm(edge_index, num_nodes, edge_weight=None, normalization='sym', lambda_max=None, batch=None)

graph laplacian normalization

Parameters

• edge_index (Tensor) – Edge index. The shape is \((2, N\_e)\) where \(N\_e\) is the number of edges.

• num_nodes (int) – Number of nodes.

• edge_weight (Tensor) – Edge weights. The shape is \((N\_e)\) where \(N\_e\) is the number of edges. Default: dense.

• normalization (str) –

  Normalization method. Default: ‘sym’. \((L)\) is normalized matrix, \((D)\) is degree matrix, \((A)\) is adjaceny matrix, \((I)\) is unit matrix.

  1. None: No normalization \(\mathbf{L} = \mathbf{D} - \mathbf{A}\)

  2. ’sym’: Symmetric normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}\)

  3. ’rw’: Random-walk normalization \(\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1} \mathbf{A}\)

• lambda_max (int, float) – Lambda value of graph. Default: dense.

• batch (Tensor) – Batch vector. Default: dense.

Returns

• edge_index (Tensor) - normalized edge_index.

• edge_weight (Tensor) - normalized edge_weight

Raises

ValueError – if normalization not is None or ‘sym’ or ‘rw’.

Supported Platforms:

Ascend GPU

Examples

>>> import mindspore as ms
>>> from mindspore_gl.graph import norm
>>> edge_index = [[1, 1, 2, 2], [0, 2, 0, 1]]
>>> edge_index = ms.Tensor(edge_index, ms.int32)
>>> num_nodes = 3
>>> edge_index, edge_weight = norm(edge_index, num_nodes)
>>> print(edge_index)
[[1 1 2 2 0 1 2]
 [0 2 0 1 0 1 2]]
>>> print(edge_weight)
[-0.        -0.4999999 -0.        -0.4999999  1.         1.
  1.       ]