  Graph serves as a powerful tool for modeling data that has an underlying
structure in non-Euclidean space, by encoding relations as edges and entities
as nodes. Despite developments in learning from graph-structured data over the
years, one obstacle persists: graph imbalance. Although several attempts have
been made to target this problem, they are limited to considering only
class-level imbalance. In this work, we argue that for graphs, the imbalance is
likely to exist at the sub-class topology group level. Due to the flexibility
of topology structures, graphs could be highly diverse, and learning a
generalizable classification boundary would be difficult. Therefore, several
majority topology groups may dominate the learning process, rendering others
under-represented. To address this problem, we propose a new framework
{\method} and design (1 a topology extractor, which automatically identifies
the topology group for each instance with explicit memory cells, (2 a training
modulator, which modulates the learning process of the target GNN model to
prevent the case of topology-group-wise under-representation. {\method} can be
used as a key component in GNN models to improve their performances under the
data imbalance setting. Analyses on both topology-level imbalance and the
proposed {\method} are provided theoretically, and we empirically verify its
effectiveness with both node-level and graph-level classification as the target
tasks.
