We study how different types of social connections between people shape their social network. There are two possible types of ties between individuals, strong and weak, that differ in maintenance costs and reliability. A network formation game is played in which agents choose the number of ties of each type to maximize their chances of hearing about a job opportunity. We find that in equilibrium, people maintain both types of connections. Furthermore, in the socially optimal symmetric network there are more strong ties than in the equilibrium one.