Graph level RNN use RNN to capture graph level pattern, such as temporal pattern of dynamic graph and sequential pattern under different graph granularities. 

An example under this category is Dynamic Graph Neural Network (DGNN). DGNN can capture the temporal pattern of a dynamic graph. When a new edge is added to the graph, it uses LSTM to update the two newly connected nodes and their immediate neighbors.

University of Notre Dame

RNN is a class of neural network models that model sequential data. Examples include Gated Recurrent Units (GRU) or Long Short-Term Memory (LSTM) model. RNN can be adapted to graph modeling with some moderate modification.

Graph Recurrent Neural Networks (RNN)

Zhang, Z., Cui, P., & Zhu, W. (2020). Deep learning on graphs: A survey. IEEE Transactions on Knowledge and Data Engineering.

Deep Learning on Graphs: A Survey

Under node level graph RNN, each node is represented as a lower dimension vector, and the vector for each node is an aggregation of vectors of its neighbor node. And this aggregation is repeated multiple times to encode graph structure information in node representation. 

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