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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

A Comprehensive Review of Propagation Models in Complex Networks: From Deterministic to Deep Learning Approaches

Journal of Vibration Testing and System Dynamics 9(2) (2025) 187--208 | DOI:10.5890/JVTSD.2025.06.009

Bin Wu$^{1}$, Sifu Luo$^{2}$, C Steve Suh$^{1}$

$^{1}$ Department of Mechanical Engineering, Texas A&M University, College Station, TX 778406, USA

$^{2}$ Department of Physics & Astronomy, Texas A&M University, College Station, TX 778406, USA

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Abstract

Understanding the mechanisms of propagation in complex networks is critical for various domains such as epidemiology, social media, communication networks, and multi-robot systems. This paper provides a comprehensive review of propagation models in complex networks, ranging from traditional deterministic models to advanced data-driven and deep learning approaches. We first discuss static and dynamic network structures, noting that static models offer foundational insights into network behavior, while dynamic models capture the time-evolving nature of real-world systems. Deterministic models, such as the SIR framework, provide clear mathematical formulations for describing the spread of information and viruses, but they often lack flexibility in dealing with real-world randomness. In contrast, stochastic models introduce randomness, making simulations of network behaviors more realistic, albeit at the expense of interpretability. Behavior-based models, including agent-based simulations, focus on individual decision-making processes, offering greater flexibility but requiring significant computational resources. Data-driven approaches leverage large datasets to adapt to changing network environments, improving accuracy in nonlinear and dynamic scenarios. These approaches can rely on the aforementioned models or be based on model-free machine learning methods. We then explore supervised learning methods that require large amounts of labeled data, and unsupervised learning methods, which do not rely on labeled data. These two methods are the most mainstream approaches in machine learning. Building on this, we further investigate reinforcement learning, a newer learning paradigm that interacts with environments and does not require datasets. Finally, we specifically discuss the application of graph neural networks (GNNs), which are closely aligned with network problems and have achieved revolutionary progress in modeling and optimizing propagation capabilities in large-scale and complex networks. The paper highlights key applications and challenges for each model type and emphasizes the growing role of hybrid and machine learning-based models in solving modern network propagation problems.

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