Dynamic diffusion in complex network structures explain the spread of information, diseases, behaviors, innovations and signals across interconnected systems. Network diffusion is highly reliant on topology, heterogeneity of nodes, clustering, modularity, and temporal dynamics as opposed to classical diffusion in continuous media. This is a review of theoretical backgrounds, mathematical models, structural determinants, and interdisciplinary applications of diffusion processes in complex networks. The main analysis tool is given by the graph theory in which the network Laplacian dictates diffusion and random walks as a stochastic process. Contagion dynamics are described by epidemiological models, such as SIR model and SIS model whilst the social influence spreading is described by threshold and cascade models. Such structural features as the scale-free topology, small-world phenomena outlined by the Watts-Strogatz model and the structure of communities have a great impact on the velocity and stability of spread. The other characteristics noted in the review include multilayer and temporal networks, computational simulations, and uses in epidemiology, neuroscience, finance and social media. The newer trends are an increased level of interaction and predictive modeling with AI. Diffusion in complex networks. It is fundamental to understand that people can design effective interventions and enhance resilience in interconnected systems.
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