We propose some simple models of the growth of social networks, based on three general principles: (1) meetings take place between pairs of individuals at a rate which is high if a pair has one or more mutual friends and low otherwise; (2) acquaintances between pairs of individuals who rarely meet decay over time; (3) there is an upper limit on the number of friendships an individual can maintain. using computer simulations, we find that models that incorporatge all of these features reproduce many of the features of real social networks, including high levels of clustering or network transitivity and strong community structure in which individuals have more links to others within their community than to individuals from other communities.