We consider a network of players endowed with individual preferences and involved in interactions of various patterns. We show that their ability to make choices according to their preferences is limited, in a specific way, by their involvement in the network. The earlier literature demonstrated the conflict between individuality and peer pressure. We show that such a conflict is also present in contexts in which players do not necessarily aim at conformity with their peers. We investigate the consequences of preference heterogeneity for different interaction patterns, characterize corresponding equilibria and outline the class of games in which following own preferences is the unique Nash equilibrium. The introduction of personal preferences changes equilibrium outcomes in a non-trivial fashion: some equilibria disappear, while other, qualitatively new, appear. These results are robust to both independent and interdependent relationship between personal and social utility components.