  Graph Transformers (GTs) have made remarkable achievements in graph-level
tasks. However, most existing works regard graph structures as a form of
guidance or bias for enhancing node representations, which focuses on
node-central perspectives and lacks explicit representations of edges and
structures. One natural question is, can we treat graph structures node-like as
a whole to learn high-level features? Through experimental analysis, we explore
the feasibility of this assumption. Based on our findings, we propose a novel
multi-view graph representation learning model via structure-aware searching
and coarsening (GRLsc) on GT architecture for graph classification.
Specifically, we build three unique views, original, coarsening, and
conversion, to learn a thorough structural representation. We compress loops
and cliques via hierarchical heuristic graph coarsening and restrict them with
well-designed constraints, which builds the coarsening view to learn high-level
interactions between structures. We also introduce line graphs for edge
embeddings and switch to edge-central perspective to construct the conversion
view. Experiments on eight real-world datasets demonstrate the improvements of
GRLsc over 28 baselines from various architectures.
