Yu He

Alexandre Benoit, Catherine Aitken, Yu He

Graph rewiring has emerged as a key technique to alleviate over-squashing in Graph Neural Networks (GNNs) and Graph Transformers by modifying the graph topology to improve information flow. While effective, rewiring inherently alters the graph's structure, raising the risk of distorting important topology-dependent signals. Yet, despite the growing use of rewiring, little is known about which structural properties must be preserved to ensure both performance gains and structural fidelity. In this work, we provide the first systematic analysis of how rewiring affects a range of graph structural metrics, and how these changes relate to downstream task performance. We study seven diverse rewiring strategies and correlate changes in local and global graph properties with node classification accuracy. Our results reveal a consistent pattern: successful rewiring methods tend to preserve local structure while allowing for flexibility in global connectivity. These findings offer new insights into the design of effective rewiring strategies, bridging the gap between graph theory and practical GNN optimization.

He Yu, Jing Liu

Community structures are critical for understanding the mesoscopic organization of networks, bridging local and global patterns. While methods such as DeepWalk and node2vec capture local positional information through random walks, they fail to preserve community structures. Other approaches like modularized nonnegative matrix factorization and evolutionary algorithms address this gap but are computationally expensive and unsuitable for large-scale networks. To overcome these limitations, we propose Two Layer Walk (TLWalk), a novel graph embedding algorithm that incorporates hierarchical community structures. TLWalk balances intra- and inter-community relationships through a community-aware random walk mechanism without requiring additional parameters. Theoretical analysis demonstrates that TLWalk effectively mitigates locality bias. Experiments on benchmark datasets show that TLWalk outperforms state-of-the-art methods, achieving up to 3.2% accuracy gains for link prediction tasks. By encoding dense local and sparse global structures, TLWalk proves robust and scalable across diverse networks, offering an efficient solution for network analysis.