This paper investigates distributed flocking problem where the information exchange among agents is modeled by the communication topology changing with time. Previous research on this problem establishes group stabilization by assuming that the dynamic topology is connected all the time, which however cannot be guaranteed by most proposed distributed control laws. In this paper, a distributed algorithm to distill a necessary subgraph of the initial communication topology is presented.This subgraph covers all the vertices of the communication topology and is proved to be connected as long as the initial communication topology is connected. A distributed control law is then designed to pursue the flocking motion while preserving all the edges in this subgraph. In this way, connectivity can be preserved all the time, and flocking problem is thus solved only provided the initial communication topology of multi-agent system is connected.