  Social network analysis faces profound difficulties in sharing data between
researchers due to privacy and security concerns. A potential remedy to this
issue are synthetic networks, that closely resemble their real counterparts,
but can be freely distributed. generating synthetic networks requires the
creation of network topologies that, in application, function as realistically
as possible. Widely applied models are currently rule-based and can struggle to
reproduce structural dynamics. Lead by recent developments in Graph Neural
Network (GNN) models for network generation we evaluate the potential of GNNs
for synthetic social networks. Our GNN use is specifically within a reasonable
use-case and includes empirical evaluation using Maximum Mean Discrepancy
(MMD). We include social network specific measurements which allow evaluation
of how realistically synthetic networks behave in typical social network
analysis applications.
  We find that the Gated Recurrent Attention Network (GRAN) extends well to
social networks, and in comparison to a benchmark popular rule-based generation
Recursive-MATrix (R-MAT) method, is better able to replicate realistic
structural dynamics. We find that GRAN is more computationally costly than
R-MAT, but is not excessively costly to employ, so would be effective for
researchers seeking to create datasets of synthetic social networks.
