The key benefit of the GRAN model, compared to GraphRNN, is that it does not need to maintain a long and complex history in a graph-level RNN. Instead, the GRAN model explicitly conditions on the already generated graph using a GNN at each generation step.

Key Benefit of the GRAN Model

The GRAN model can be trained in an analogous manner as GraphRNN
by maximizing the likelihood of training graphs using teacher forcing. Like the GraphRNN model, we must also specify an ordering over nodes to compute the likelihood on training graphs. Lastly, like the GraphRNN model, we can use GRAN as a generative model after training simply by running the stochastic generation process.

Similarities between GraphGNN and GRAN

To address some of the limitations of the GraphRNN approach, GRAN model was proposed. GRAN maintains the autoregressive decomposition of the generation process, and instead of using RNNs to model the autoregressive generation process, GRAN uses GNNs. The key idea in GRAN is that we can model the conditional distribution of each row of the adjacency matrix by running a GNN on the graph that has been generated so far.

Hamilton College

There are two concrete instantiations of the autoregressive generation
idea: in the first model called GraphRNN, we model autoregressive dependencies using a recurrent neural network (RNN); In the second approach called graph recurrent attention network (GRAN), we generate graphs by using a GNN to condition on the adjacency matrix that has been generated so far.

Recurrent Models for Graph Generation

Hamilton, W.L. Graph Representation Learning. *Synthesis Lectures on Artificial Intelligence and Machine Learning*. 2020, 14(3), 1–159. https://doi.org/10.2200/S01045ED1V01Y202009AIM046

Graph Representation Learning by William Hamilton

The basic idea in the GraphRNN approach is to use a hierarchical RNN to model the edge dependencies in the equation shown below. The first RNN in the hierarchical model is used to model the state of the graph that has been generated so far. The second RNN generates the entries of L[vi, :] in an autoregressive manner. The overall GraphRNN approach is called hierarchical because the node-level RNN is initialized at each time-step with the current hidden state of the graph-level RNN.

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