NSPG: A Personalized Gravity Model with Adaptive Gravity Coefficients for Relative Importance Mining

Mining relatively important nodes with respect to known significant nodes in complex networks is a pivotal branch of node importance research, with promising applications ranging from epidemic risk inference to disease-gene prioritization. Among existing approaches, integrating network embedding with the gravity model offers an attractive framework, as its multiplicative form aggregates pairwise proximity and influence without iterative convergence. Nevertheless, the aforementioned approaches evaluate the seed set strictly on a per-node basis, thereby neglecting the collective influence of the seed set as an integrated entity—namely, its aggregate multi-hop reachability relative to a given candidate node. To address these issues, this paper proposes NSPG (Network Semantic PageRank Gravity), which refines the gravity model in two aspects. First, it replaces mass construction with a temperature-scaled exponential of the cosine similarity. This term is derived from the same embedding geometry as the Euclidean distance in the denominator, yet it captures only the relative aspect of similarity, while the denominator captures the absolute aspect. Second, it employs personalized PageRank as a seed-conditioned gravitational coefficient, which quantifies the candidate node’s aggregate multi-hop proximity to the seed set as a whole. Experiments on undirected, unweighted, static networks show that NSPG achieves superior or comparable performance. Moreover, the model remains robust across various experimental settings, owing to the complementarity of the numerator and denominator: they form a static embedding-geometric layer that anchors the scores, while the PPR coefficient acts as a seed-conditioned layer that adapts to seed variation.