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

Bin Wu, Sifu Luo, C. Steve Suh

TL;DR

This survey analyzes propagation models in complex networks across static and dynamic contexts, spanning deterministic, stochastic, behavior-based, and data-driven model-based approaches as well as model-free paradigms such as supervised, unsupervised, reinforcement learning, and graph neural networks. It highlights the tradeoffs between interpretability, realism, data requirements, and computational cost, and emphasizes the role of hybrid and data-driven strategies to address dynamic networks. Core contributions include a taxonomy of propagation models, representative mathematical formulations (e.g., SIR, random walks, ABMs, GANs, GCNs), and a synthesis of applications and challenges across epidemiology, communication, and multi-robot systems. The practical impact lies in guiding researchers to select and combine methods for accurate, scalable propagation analysis and control in real-world, time-evolving networks.

Abstract

Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven and deep learning approaches. We differentiate between static and dynamic networks, noting that static models provide foundational insights, while dynamic models capture real-world temporal changes. Deterministic models like the SIR framework offer clear mathematical insights but often lack adaptability to randomness, whereas stochastic models enhance realism at the cost of interpretability. Behavior-based models focus on individual decision-making, demanding more computational resources. Data-driven approaches improve accuracy in nonlinear scenarios by adapting to evolving networks, using either traditional models or model-free machine learning techniques. We explore supervised and unsupervised learning methods, as well as reinforcement learning, which operates without predefined datasets. The application of graph neural networks (GNNs) is also discussed, highlighting their effectiveness in modeling propagation in complex networks. The paper underscores key applications and challenges associated with each model type, emphasizing the increasing importance of hybrid and machine learning-based solutions in contemporary network propagation issues.

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

TL;DR

This survey analyzes propagation models in complex networks across static and dynamic contexts, spanning deterministic, stochastic, behavior-based, and data-driven model-based approaches as well as model-free paradigms such as supervised, unsupervised, reinforcement learning, and graph neural networks. It highlights the tradeoffs between interpretability, realism, data requirements, and computational cost, and emphasizes the role of hybrid and data-driven strategies to address dynamic networks. Core contributions include a taxonomy of propagation models, representative mathematical formulations (e.g., SIR, random walks, ABMs, GANs, GCNs), and a synthesis of applications and challenges across epidemiology, communication, and multi-robot systems. The practical impact lies in guiding researchers to select and combine methods for accurate, scalable propagation analysis and control in real-world, time-evolving networks.

Abstract

Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven and deep learning approaches. We differentiate between static and dynamic networks, noting that static models provide foundational insights, while dynamic models capture real-world temporal changes. Deterministic models like the SIR framework offer clear mathematical insights but often lack adaptability to randomness, whereas stochastic models enhance realism at the cost of interpretability. Behavior-based models focus on individual decision-making, demanding more computational resources. Data-driven approaches improve accuracy in nonlinear scenarios by adapting to evolving networks, using either traditional models or model-free machine learning techniques. We explore supervised and unsupervised learning methods, as well as reinforcement learning, which operates without predefined datasets. The application of graph neural networks (GNNs) is also discussed, highlighting their effectiveness in modeling propagation in complex networks. The paper underscores key applications and challenges associated with each model type, emphasizing the increasing importance of hybrid and machine learning-based solutions in contemporary network propagation issues.
Paper Structure (14 sections, 20 equations, 7 figures)

This paper contains 14 sections, 20 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Overview of Propagation Problem in Complex Network
  3. Model Based Method
  4. Deterministic Model
  5. Stochastic Model
  6. Behavior Based Model
  7. Data-Driven Models
  8. Model-Free Method
  9. Supervised Learning
  10. Unsupervised Learning
  11. Reinforcement Learning
  12. Graph Neural Network
  13. Applications and Challenges
  14. Conclusion

Figures (7)

  • Figure 1: Dynamic network evolving with time
  • Figure 2: The characteristics of the nodes in the contact network and the undirected graph.
  • Figure 3: Relationship and Overlap Between Different Model-based and Model-free Approaches
  • Figure 4: Comparison of Model-based Methods for Network Propagation
  • Figure 5: Comparison of Model-free Methods for Network Propagation
  • ...and 2 more figures