Social network structures play an important role in the lives of animals by affecting individual fitness and the spread of disease and information. Nevertheless, we still lack a good understanding of how these structures emerge from the behavior of individuals. Generative network models provide a powerful approach that can help close this gap. Empirical research has shown that trait-based social preferences (preferences for social partners with certain trait values, such as sex, body size, relatedness etc.) play a key role in the formation of social networks across species. Currently, however, we lack a good understanding of how such preferences affect network properties. In this study: 1) we develop a general and flexible generative network model that can create artificial (simulated) networks where social connection is affected by trait-based social preferences; 2) we use this model to investigate how different trait-based social preferences affect social network structure and function. We find that the preferences can affect the efficiency of the networks in terms of transmitting disease and information, and their robustness against fragmentation when individuals disappear, with the effects often - but not always - going in the direction of slower transmission and lower robustness. Furthermore, the extent and form of the effects depend on both the type of preference and the type of trait it is used with. The findings lead to new insights about the potential mechanisms driving the structural diversity of animal social networks, the importance of trait value distributions for social structure, the degree distributions of social networks, and the detectability of trait effects from network data. Overall, the study shows that trait-based social preferences can have far-reaching consequences for populations.