This paper studies a noncooperative model of network formation. Built upon the two-way flow model of Bala and Goyal (2000a), it assumes that information decay as it flows through each agent, and the decay is increasing and concave in the number of his links. This assumption results in the fact that a large set of Nash networks are disconnected and consist of components of different sizes, a feature that resembles that of real-world networks. Discussions on this insight are provided.