  Graph Convolutional Networks (GCNs) can capture non-Euclidean spatial
dependence between different brain regions. The graph pooling operator, a
crucial element of GCNs, enhances the representation learning capability and
facilitates the acquisition of abnormal brain maps. However, most existing
research designs graph pooling operators solely from the perspective of nodes
while disregarding the original edge features. This confines graph pooling
application scenarios and diminishes its ability to capture critical
substructures. In this paper, we propose a novel edge-aware hard clustering
graph pool (EHCPool), which is tailored to dominant edge features and redefines
the clustering process. EHCPool initially introduced the 'Edge-to-Node' score
criterion which utilized edge information to evaluate the significance of
nodes. An innovative Iteration n-top strategy was then developed, guided by
edge scores, to adaptively learn sparse hard clustering assignments for graphs.
Additionally, a N-E Aggregation strategy is designed to aggregate node and edge
features in each independent subgraph. Extensive experiments on the multi-site
public datasets demonstrate the superiority and robustness of the proposed
model. More notably, EHCPool has the potential to probe different types of
dysfunctional brain networks from a data-driven perspective. Method code:
https://github.com/swfen/EHCPool
