class dgl.nn.pytorch.conv.GCN2Conv(in_feats, layer, alpha=0.1, lambda_=1, project_initial_features=True, allow_zero_in_degree=False, bias=True, activation=None)[source]

Bases: torch.nn.modules.module.Module

Graph Convolutional Network via Initial residual and Identity mapping (GCNII) from Simple and Deep Graph Convolutional Networks

It is mathematically is defined as follows:

\[\mathbf{h}^{(l+1)} =\left( (1 - \alpha)(\mathbf{D}^{-1/2} \mathbf{\hat{A}} \mathbf{D}^{-1/2})\mathbf{h}^{(l)} + \alpha {\mathbf{h}^{(0)}} \right) \left( (1 - \beta_l) \mathbf{I} + \beta_l \mathbf{W} \right)\]

where \(\mathbf{\hat{A}}\) is the adjacency matrix with self-loops, \(\mathbf{D}_{ii} = \sum_{j=0} \mathbf{A}_{ij}\) is its diagonal degree matrix, \(\mathbf{h}^{(0)}\) is the initial node features, \(\mathbf{h}^{(l)}\) is the feature of layer \(l\), \(\alpha\) is the fraction of initial node features, and \(\beta_l\) is the hyperparameter to tune the strength of identity mapping. It is defined by \(\beta_l = \log(\frac{\lambda}{l}+1)\approx\frac{\lambda}{l}\), where \(\lambda\) is a hyperparameter. \(\beta\) ensures that the decay of the weight matrix adaptively increases as we stack more layers.

  • in_feats (int) – Input feature size; i.e, the number of dimensions of \(h_j^{(l)}\).

  • layer (int) – the index of current layer.

  • alpha (float) – The fraction of the initial input features. Default: 0.1

  • lambda_ (float) – The hyperparameter to ensure the decay of the weight matrix adaptively increases. Default: 1

  • project_initial_features (bool) – Whether to share a weight matrix between initial features and smoothed features. Default: True

  • bias (bool, optional) – If True, adds a learnable bias to the output. Default: True.

  • activation (callable activation function/layer or None, optional) – If not None, applies an activation function to the updated node features. Default: None.

  • allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.


Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph
>>> g = dgl.add_self_loop(g)

Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.


>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GCN2Conv
>>> # Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 3)
>>> g = dgl.add_self_loop(g)
>>> conv1 = GCN2Conv(3, layer=1, alpha=0.5, \
...         project_initial_features=True, allow_zero_in_degree=True)
>>> conv2 = GCN2Conv(3, layer=2, alpha=0.5, \
...         project_initial_features=True, allow_zero_in_degree=True)
>>> res = feat
>>> res = conv1(g, res, feat)
>>> res = conv2(g, res, feat)
>>> print(res)
tensor([[1.3803, 3.3191, 2.9572],
        [1.3803, 3.3191, 2.9572],
        [1.3803, 3.3191, 2.9572],
        [1.4770, 3.8326, 3.2451],
        [1.3623, 3.2102, 2.8679],
        [1.3803, 3.3191, 2.9572]], grad_fn=<AddBackward0>)
forward(graph, feat, feat_0, edge_weight=None)[source]

Compute graph convolution.

  • graph (DGLGraph) – The graph.

  • feat (torch.Tensor) – The input feature of shape \((N, D_{in})\) where \(D_{in}\) is the size of input feature and \(N\) is the number of nodes.

  • feat_0 (torch.Tensor) – The initial feature of shape \((N, D_{in})\)

  • edge_weight (torch.Tensor, optional) – edge_weight to use in the message passing process. This is equivalent to using weighted adjacency matrix in the equation above, and \(\tilde{D}^{-1/2}\tilde{A} \tilde{D}^{-1/2}\) is based on dgl.nn.pytorch.conv.graphconv.EdgeWeightNorm.


The output feature

Return type



DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.


  • Input shape: \((N, *, \text{in_feats})\) where * means any number of additional dimensions, \(N\) is the number of nodes.

  • Output shape: \((N, *, \text{out_feats})\) where all but the last dimension are the same shape as the input.

  • Weight shape: \((\text{in_feats}, \text{out_feats})\).


Reinitialize learnable parameters.