In this paper we present a new conceptual framework to model diffusion processes in networks. Our approach is to exploit dynamic network flow theory to model the dynamics of time-dependent diffusion processes in networked systems. In contrast to traditional network flow theory that emphasizes the optimization of network flows in the presence of capacity constraints, our objective is to build quantitative models of time-dependent network flow evolution. We derive systems of coupled differential equations whose solutions describe network flow dynamics, and apply the theory to study frequently occuring network process classes. The theory developed in this article is applicable to numerous problem domains where phenomena can be modeled by dynamically changing network flows, such as problems of logistical systems, transportation and traffic flow analysis, the study of information flow in communication systems and social networks, processes of information, innovation and meme diffusion, memetics, marketing theory and other fields.
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