class_docstr: Output:
      node representations
code: def forward(self, g, x, edge_attr):
      ### virtual node embeddings for graphs
      virtualnode_embedding = self.virtualnode_embedding(
          torch.zeros(g.batch_size).to(x.dtype).to(x.device)
      )
  
      h_list = [self.atom_encoder(x)]
      batch_id = dgl.broadcast_nodes(
          g, torch.arange(g.batch_size).to(x.device)
      )
      for layer in range(self.num_layers):
          ### add message from virtual nodes to graph nodes
          h_list[layer] = (
              h_list[layer] + virtualnode_embedding[batch_id]
          )
  
          ### Message passing among graph nodes
          h = self.convs[layer](g, h_list[layer], edge_attr)
          h = self.batch_norms[layer](h)
          if layer == self.num_layers - 1:
              # remove relu for the last layer
              h = F.dropout(h, self.drop_ratio, training=self.training)
          else:
              h = F.dropout(
                  F.relu(h), self.drop_ratio, training=self.training
              )
  
          if self.residual:
              h = h + h_list[layer]
  
          h_list.append(h)
  
          ### update the virtual nodes
          if layer < self.num_layers - 1:
              ### add message from graph nodes to virtual nodes
              virtualnode_embedding_temp = (
                  self.pool(g, h_list[layer]) + virtualnode_embedding
              )
              ### transform virtual nodes using MLP
              virtualnode_embedding_temp = self.mlp_virtualnode_list[
                  layer
              ](virtualnode_embedding_temp)
  
              if self.residual:
                  virtualnode_embedding = (
                      virtualnode_embedding
                      + F.dropout(
                          virtualnode_embedding_temp,
                          self.drop_ratio,
                          training=self.training,
                      )
                  )
              else:
                  virtualnode_embedding = F.dropout(
                      virtualnode_embedding_temp,
                      self.drop_ratio,
                      training=self.training,
                  )
  
      ### Different implementations of Jk-concat
      if self.JK == "last":
          node_representation = h_list[-1]
      elif self.JK == "sum":
          node_representation = 0
          for layer in range(self.num_layers):
              node_representation += h_list[layer]
  
      return node_representation
  
imports: import dgl
  import dgl.function
  import torch
  import torch.nn
  import torch.nn.functional
  from dgl.nn.pytorch import SumPooling
  from ogb.graphproppred.mol_encoder import AtomEncoder, BondEncoder
label_desc: Use image node_id 2 for calling the GNN_node_Virtualnode obj's underlying member method code with example usage: obj.forward(g, x, edge_attr) and returns: node_representation