We study the diffusion of an idea, a product, a disease, a cultural fad, or a technology among agents in a social network that exhibits segregation or homophily (the tendency of agents to associate with others similar to themselves). Individuals are distinguished by their types - e.g., race, gender, age, wealth, religion, profession - which, together with biased interaction patterns, induce heterogeneous rates of adoption or infection. We identify the conditions under which a behavior or disease diffuses and becomes persistent in the population. These conditions relate to the level of homophily in a society and the underlying proclivities of various types for adoption or infection. In particular, we show that homophily can facilitate diffusion from a small initial seed of adopters.
Jackson, M. O., & Lopez-Pintado, D. (2013). Diffusion and contagion in networks with heterogeneous agents and homophily. Network Science (New York), 1(1), 49-67. https://doi.org/10.1017/nws.2012.7 (Original work published 2013)