Percolation in homophilious social networks

In network theory, homophily is a tendency to connections between nodes of similar characteristics. Social networks, such as friendship networks, tend to be homophilious, since they connect individuals of similar tastes or opinions. The effect of homophily and information diffusion in social networks are difficult to distinguish in empirical studies: an homophilious network might display a behavior similar to diffusion through word-of-mouth just because agents with similar characteristics are likely to both adopt similar things and be connected to each other. The objective of this study is to analyze the effect of homophily in diffusion by word-of-mouth and to compare it with a non-homophilious benchmark. We introduce homophily in a percolation model of word-of-mouth diffusion as a modification of the small world algorithm. This novel algorithm reorganizes the nodes according to their individual characteristics, so the resulting network is highly homophilious. A comparison between diffusion in the modified network and in the benchmark scenario allows to isolate the effect of homophily in adoption. The main result is that homophily reduces the effect of the network structure: homophilious networks with different link structures present almost identical adoption sizes. In other words, the diffusion size does not differ substantially for different values of the rewiring probability. This is equivalent to saying that the network structure of a population does not play much of a role in this context. This effect results from the extreme case of homophily considered. Nonetheless, this novel approach to introduce homophily in a social network allows for an intuitive development of the word-of-mouth diffusion process in homophilious networks. The prevalence of homophily in social networks calls for studies that introduce homophily in simulation models of diffusion such as this.