  Recent research in the field of graph neural network (GNN) has identified a
critical issue known as "over-squashing," resulting from the bottleneck
phenomenon in graph structures, which impedes the propagation of long-range
information. Prior works have proposed a variety of graph rewiring concepts
that aim at optimizing the spatial or spectral properties of graphs to promote
the signal propagation. However, such approaches inevitably deteriorate the
original graph topology, which may lead to a distortion of information flow. To
address this, we introduce an expanded width-aware (PANDA) message passing, a
new message passing paradigm where nodes with high centrality, a potential
source of over-squashing, are selectively expanded in width to encapsulate the
growing influx of signals from distant nodes. Experimental results show that
our method outperforms existing rewiring methods, suggesting that selectively
expanding the hidden state of nodes can be a compelling alternative to graph
rewiring for addressing the over-squashing.
