In this work, we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. Then we study diffusion on network models that have overlapping community structure. We study both contagions in the standard SIR model, and complex contagions which are thought to be better approximations of some social diffusion processes. Finally, we investigate diffusion on empirical networks with known overlapping community structure, by analysing the structure of such networks, and by simulating contagion on them. Our results show that simple and complex contagions can spread fast in networks with overlapping community structure.
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