The GraphRNN model still generates unrealistic artifacts (e.g., long chains) when trained on samples of grids. Moreover, GraphRNN can be difficult to train and scale to large graphs due to the need to back-propagate through many steps of RNN recurrence.

Limitations of GraphRNN

The key benefit of the GraphRNN approach is that it models dependencies between edges. Using an autoregressive modeling assumption, GraphRNN can condition the generation of edges at generation step i based on the state of the graph that has already been generated during generation steps 1, ...i − 1, which makes it much easier to generate complex motifs and regular graph structures, such as grids.

Key Benefit of GraphRNN

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.

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

GraphRNN

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.

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