  Generative graph models create instances of graphs that mimic the properties
of real-world networks. Generative models are successful at retaining pairwise
associations in the underlying networks but often fail to capture higher-order
connectivity patterns known as network motifs. Different types of graphs
contain different network motifs, an example of which are triangles that often
arise in social and biological networks. It is hence vital to capture these
higher-order structures to simulate real-world networks accurately. We propose
Multi-MotifGAN (MMGAN), a motif-targeted Generative Adversarial Network (GAN)
that generalizes the benchmark NetGAN approach. The generalization consists of
combining multiple biased random walks, each of which captures a different
motif structure. MMGAN outperforms NetGAN at creating new graphs that
accurately reflect the network motif statistics of input graphs such as
Citeseer, Cora and Facebook.
