This paper analyzes how social structure and social pressure affect the diffusion of an idea in a population of human agents. The diffusion process of ideas shares several features and factors with diffusion of new technologies and products (Centola 2010 , Campbell 2013 ). A percolation model of diffusion (Solomon et al 2000) assumes that information is local and embedded in a social network. The structure of the network is, thus, decisive to the success or failure of diffusion. We focus on small world networks (Watts and Strogatz 1998 ) and stud y how diffusion scales with the density of network short - cuts . We introduce social pressure and assortativity in the model and study how they affect the diffusion process. Our numerical analysis shows that social pressure cannot be ignored when studying the diffusion of ideas, as it severely affects the output of the process. Some ideas with an original value so low that it would never get diffused can be spread due to the strength of social pressure. This effect interacts with the structure of the network - it is larger for small rewiring probabilities . Also, social pressure deeply influences the effect of clustering links. Clusters are useless - when not harmful - in a percolation model of diffusion, since most of their links convey redundant information. Social pressure completely changes the picture, because sequential adoption of neighbors can make one agent adopt at later stages. Finally, assortativity is found to favor diffusion, as it allows information to be spread to the “right agents” .