A multi-spacecraft system consists of wirelessly-connected spacecraft that share resources in Earth orbit or deep space. One of the enabling technologies of such a fractionated space architecture is cluster flight, which provides the cluster with the capability to perform a cluster scatter and regather maneuvers to rapidly evade debris-like threats or to reconfigure for scientific missions. In this work, we study the cluster reconfiguration problem. First, we propose an algorithm based on semidefinite programming to check for the feasibility of a desired configuration. Next, we provide a control law for cluster reconfiguration that requires only relative state information and the adjacency matrix of the underlying network topology. Stability analysis and simulation results are provided.