  We study how a behavior (an idea, buying a product, having a disease,
adopting a cultural fad or a technology) spreads among agents in an 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, etc.)
which, together with biased interaction patterns, induce heterogeneous rates of
adoption. We identify the conditions under which a behavior diffuses and
becomes persistent in the population. These conditions relate to the level of
homophily in a society, the underlying proclivities of various types for
adoption or infection, as well as how each type interacts with its own type. In
particular, we show that homophily can facilitate diffusion from a small
initial seed of adopters.
