## 2 Related Work  
### Information Diffusion Models  
Information diffusion in social networks has attracted substantial research attention over the past two decades. As comprehensively documented in the state-of-the-art review by [PERSON] et al. (2022) [3], this field has evolved from basic epidemic models to sophisticated approaches incorporating temporal dynamics, network topology, and behavioral factors. This extensive review provides a valuable framework for understanding the spectrum of diffusion models and their applications for various social network vulnerabilities. Our work builds upon this rich foundation while focusing specifically on delay mechanisms in information propagation. The theoretical foundations of information diffusion modeling were established by several seminal works. [PERSON] et al. (2003) [4] introduced the fundamental problem of influence maximization in social networks, proposing the now-classical Independent Cascade (IC) and Linear Threshold (LT) models. Their work proved the NP-hardness of the influence maximization problem and developed a greedy approximation algorithm with theoretical guarantees, which continues to influence optimization approaches in network diffusion. Building on this foundation, [PERSON] et al. (2007) [5] conducted empirical studies of information cascades in large blog networks, revealing characteristic patterns in how information propagates. Their analysis identified distinct cascade structures and temporal dynamics that have informed numerous subsequent studies on information spread, establishing methodological principles for the empirical analysis of diffusion processes. A significant advancement in temporal modeling came from [PERSON] et al. (2010) [6], who introduced a delay-aware Independent Cascade model. This approach incorporated time delays between exposure and information sharing, providing a more realistic representation of social media dynamics. Their methods for selecting appropriate diffusion models and estimating parameters from real data demonstrated the importance of temporal aspects in diffusion modeling. Further refining temporal approaches, [PERSON] (2012) [7] developed continuous-time diffusion models that enabled more precise descriptions of dynamic processes in social networks. Their analysis of competing contagions revealed that interactions between different pieces of information can significantly alter diffusion patterns, with relative changes in the spreading probability averaging at 71%. This work established a framework for understanding how multiple information streams interact during diffusion. Our research builds directly upon this intellectual lineage. While early models by [PERSON] et al. [4] and [PERSON] et al. [5] established core diffusion principles, and later advances by [PERSON] et al. [6] and [PERSON] [7] introduced temporal considerations, few studies have systematically compared different delay mechanisms across varied network structures. Our work extends these temporal approaches by specifically examining how three distinct delay types (constant, uniform, and exponential) influence information coverage across diverse network topologies. This comparative focus distinguishes our research from previous studies that typically examine a single delay model or network structure. The Susceptible-Infected-Recovered (SIR) model is widely used for information diffusion. In this model, nodes transition from susceptible to infected and finally to recovered states ([PERSON] et al., 2021) [8]. [PERSON] et al. (2020) [9] extended this approach with the Susceptible-Exposed-Infected (SEI) model by adding an intermediate \"exposed\" state. This better captures the delay between exposure to information and active sharing behavior. Recent advances in diffusion modeling have also explored the financial market implications of information spread. [PERSON] et al. (2024) [10] investigated how momentum dynamics in financial markets are influenced by information diffusion across complex social networks with different topological structures.