  Most real-world networks contain well-defined community structures where
nodes are densely connected internally within communities. To learn from these
networks, we develop MarkovGNN that captures the formation and evolution of
communities directly in different convolutional layers. Unlike most Graph
Neural Networks (GNNs) that consider a static graph at every layer, MarkovGNN
generates different stochastic matrices using a Markov process and then uses
these community-capturing matrices in different layers. MarkovGNN is a general
approach that could be used with most existing GNNs. We experimentally show
that MarkovGNN outperforms other GNNs for clustering, node classification, and
visualization tasks. The source code of MarkovGNN is publicly available at
\url{https://github.com/HipGraph/MarkovGNN}.
