AMPS: A Direction-Aware Adaptive Multi-Scale Potential Model for Link Prediction in Complex Networks

To overcome the limitations of current link prediction methods in effectively leveraging topological information and node importance, this paper introduces a new model called AMPS (Adaptive Multi-scale Potential-enhanced Path Similarity). The model is built on a hierarchical structure that captures both global network topology and local interaction patterns, with full compatibility for directed and undirected networks. This is achieved through a process that quantifies node potential fields, enhances multi-scale similarity, and fuses information across scales. Specifically, we define three types of potential field models, global, local, and k-hop, to flexibly measure node importance. We also introduce two complementary prediction modules: an enhanced common neighbor matrix (PCN), which uses potential fields to refine local structural details, and a feature-weighted generalized path similarity (GLP), which integrates node importance into path evaluation. The final similarity score is obtained by adaptively combining the outputs of PCN and GLP. Experiments on 12 undirected datasets and 9 directed datasets demonstrate that AMPS significantly outperforms other mainstream algorithms in terms of the AUC metric. It also exhibits strong robustness under varying training set ratios, maintaining stable advantages in both directed and undirected scenarios. This framework provides a physically intuitive, topology-aware, and high-precision solution for link prediction across various types of networks.