Abstract Creating new ties in a social network facilitates knowledge exchange and affects positional advantage. In this paper, we study the process, which we call network building, of establishing ties between two existing social networks in order to reach certain structural goals. We focus on the case when one of the two networks consists only of a single member and motivate this case from two perspectives. The first perspective is socialization: we ask how a newcomer can forge relationships with an existing network to place herself at the center. We prove that obtaining optimal solutions to this problem is NP-complete, and present several efficient algorithms to solve this problem and compare them with each other. The second perspective is network expansion: we investigate how a network may preserve or reduce its diameter through linking with a new node, hence ensuring small distance between its members. For both perspectives the experiment demonstrates that a small number of new links is usually sufficient to reach the respective goal.