  This paper introduces novel methodologies, the Distance Recomputator and
Topology Reconstructor, aimed at enhancing Graph Neural Networks (GNNs). The
Distance Recomputator dynamically recalibrates node distances within k-hop
neighborhoods using a dynamic encoding scheme, thereby improving the accuracy
and adaptability of node representations. Concurrently, the Topology
Reconstructor adjusts local graph structures based on computed "similarity
distances," optimizing network configurations for improved learning outcomes.
These methods address the limitations of static node representations and fixed
aggregation schemes in traditional GNNs, offering a more nuanced approach to
modeling complex and dynamic graph topologies.
  Furthermore, our experimental evaluations demonstrate significant performance
advantages over existing methods across various benchmark datasets. The
proposed Distance Recomputator and Topology Reconstructor not only enhance node
relationship modeling accuracy but also optimize information aggregation
efficiency through an asynchronous aggregation mechanism. This approach proves
particularly effective in scenarios involving dynamic or large-scale graphs,
showcasing the methods' robustness and applicability in real-world graph
learning tasks.
