code: def train():
      model.train()
      encoder_optimizer.zero_grad()
      z = model.encode(train_data.x, train_data.edge_index)
  
      # We optimize the discriminator more frequently than the encoder.
      for i in range(5):
          discriminator_optimizer.zero_grad()
          discriminator_loss = model.discriminator_loss(z)
          discriminator_loss.backward()
          discriminator_optimizer.step()
  
      loss = model.recon_loss(z, train_data.pos_edge_label_index)
      loss = loss + model.reg_loss(z)
      loss = loss + (1 / train_data.num_nodes) * model.kl_loss()
      loss.backward()
      encoder_optimizer.step()
      return float(loss)
  
imports: import os.path
  import matplotlib.pyplot
  import torch
  from sklearn.cluster import KMeans
  from sklearn.manifold import TSNE
  from sklearn.metrics.cluster import completeness_score, homogeneity_score, v_measure_score
  from torch.nn import Linear
  import torch_geometric.transforms
  from torch_geometric.datasets import Planetoid
  from torch_geometric.nn import ARGVA, GCNConv
label_desc: Use image node_id 1 for calling a global function with example usage: train() and returns: float