  Continual learning on graphs tackles the problem of training a graph neural
network (GNN) where graph data arrive in a streaming fashion and the model
tends to forget knowledge from previous tasks when updating with new data.
Traditional continual learning strategies such as Experience Replay can be
adapted to streaming graphs, however, these methods often face challenges such
as inefficiency in preserving graph topology and incapability of capturing the
correlation between old and new tasks. To address these challenges, we propose
TA$\mathbb{CO}$, a (t)opology-(a)ware graph (co)arsening and (co)ntinual
learning framework that stores information from previous tasks as a reduced
graph. At each time period, this reduced graph expands by combining with a new
graph and aligning shared nodes, and then it undergoes a "zoom out" process by
reduction to maintain a stable size. We design a graph coarsening algorithm
based on node representation proximities to efficiently reduce a graph and
preserve topological information. We empirically demonstrate the learning
process on the reduced graph can approximate that of the original graph. Our
experiments validate the effectiveness of the proposed framework on three
real-world datasets using different backbone GNN models.
