  Recently, there has been a surge of interest in employing neural networks for
graph generation, a fundamental statistical learning problem with critical
applications like molecule design and community analysis. However, most
approaches encounter significant limitations when generating large-scale
graphs. This is due to their requirement to output the full adjacency matrices
whose size grows quadratically with the number of nodes. In response to this
challenge, we introduce a new, simple, and scalable graph representation named
gap encoded edge list (GEEL) that has a small representation size that aligns
with the number of edges. In addition, GEEL significantly reduces the
vocabulary size by incorporating the gap encoding and bandwidth restriction
schemes. GEEL can be autoregressively generated with the incorporation of node
positional encoding, and we further extend GEEL to deal with attributed graphs
by designing a new grammar. Our findings reveal that the adoption of this
compact representation not only enhances scalability but also bolsters
performance by simplifying the graph generation process. We conduct a
comprehensive evaluation across ten non-attributed and two molecular graph
generation tasks, demonstrating the effectiveness of GEEL.
