Accurately assessing node importance in complex networks is essential for understanding critical structures and optimizing dynamic processes. Traditional gravity-based methods, which often rely on local attributes or global shortest paths, exhibit limitations in heterogeneous networks due to insuffcient differentiation of node roles and their influence across diverse topologies. To address these challenges, we propose the Bi-Dimensional Gravity Influence Model (BGIM) and its enhanced version (BGIM+). These models introduce a novel entropy-weighted gravity framework that integrates node information entropy, gravity correction factors, and asymmetric attraction factors. By replacing degree centrality with information entropy, BGIM captures nodes’ uncertainty and information richness, offering a more comprehensive view of their potential influence.
The gravity correction factor (NGCF) combines eigenvector centrality with network constraint coeffcients to balance global and local features, while the asymmetric attraction factor (AAF) accounts for gravitational asymmetry between core and peripheral nodes. This dual-dimensional approach enables a more nuanced evaluation of node importance, addressing imbalances in influence distribution across diverse network structures. A normalization mechanism further enhances adaptability, ensuring robust performance in both sparse and dense networks.
Extensive experiments on real-world (e.g., Jazz, USAir, Email, Router) and synthetic (LFR-generated) networks validate the proposed models. Results demonstrate that BGIM and BGIM+ consistently outperform classical methods such as Degree, Closeness, and Betweenness centralities in identifying critical nodes and predicting their roles in propagation dynamics. In particular, BGIM+ exhibits superior performance in networks with complex topologies, achieving high correlation with SIR (Susceptible-Infected-Recovered) model simulations under varying propagation rates. Moreover, BGIM+ effectively balances the influence of local hubs and global bridges, making it particularly suitable for heterogeneous networks.
The study highlights the significance of incorporating multidimensional features in gravity models for accurate and robust node evaluation. The proposed models advance the field of complex network analysis by providing a versatile tool for identifying influential nodes across diverse applications, including epidemic control, information dissemination, and infrastructure resilience. Future work will explore the applicability of BGIM in temporal and dynamic network contexts, further extending its utility.