  Network community detection often relies on optimizing partition quality
functions, like modularity. This optimization appears to be a complex problem
traditionally relying on discrete heuristics. And although the problem could be
reformulated as continuous optimization, direct application of the standard
optimization methods has limited efficiency in overcoming the numerous local
extrema. However, the rise of deep learning and its applications to graphs
offers new opportunities. And while graph neural networks have been used for
supervised and unsupervised learning on networks, their application to
modularity optimization has not been explored yet. This paper proposes a new
variant of the recurrent graph neural network algorithm for unsupervised
network community detection through modularity optimization. The new
algorithm's performance is compared against a popular and fast Louvain method
and a more efficient but slower Combo algorithm recently proposed by the
author. The approach also serves as a proof-of-concept for the broader
application of recurrent graph neural networks to unsupervised network
optimization.
