WDL: A Wiener-Based Diffusive Logistic Model for Information Propagation in Online Social Networks

Understanding how information spreads through online social networks is a fundamental problem in computational social science. Classical diffusion models, such as the Diffusive Logistic (DL) model, account for time and spatial dynamics, but typically assume a structurally homogeneous network. This assumption neglects the impact of network topology on diffusion patterns, which can lead to oversimplified predictions in complex social environments. In this work, we introduce (WDL) Wiener-Based Diffusive Logistic model, a topology-aware extension of the classical DL model. Our approach incorporates a structural metric known as the small Wiener index w(s,G), which quantifies the cumulative distance from a given node s to the rest of the network G. By modulating the intrinsic growth rate based on this topological centrality measure, the WDL model better captures how structural positioning influences diffusion speed and reach. We apply our model to the Higgs Twitter retweet network (SNAP dataset), extracting a subgraph around a central node and computing w(s,G) for each distance layer. Numerical simulations show that the WDL model produces heterogeneous diffusion curves: nodes closer to the center receive and propagate information faster than peripheral ones, consistent with real-world observations. These findings highlight the potential of incorporating topological indices, such as the small Wiener index, into PDE-based diffusion models to generate more realistic and adaptive predictions of information propagation in complex networks.