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In this work we study diffusion in networks with community structure. Wefirst replicate and extend work on networks with non-overlapping communitystructure. We then study diffusion on network models that have overlappingcommunity structure. We study contagions in the standard SIR model, and complexcontagions thought to be better models of some social diffusion processes.Finally, we investigate diffusion on empirical networks with known overlappingcommunity structure, by analysing the structure of such networks, and bysimulating contagion on them. We find that simple and complex contagions canspread fast in networks with overlapping community structure. We also find thatshort paths exist through overlapping community structure on empiricalnetworks.

Diffusion in Networks With Overlapping Community Structure