This paper considers the formation control problem for general linear networked agents constrained with event-triggered communications. We propose four kinds of edge-based event-triggered protocols, each of which can be used to achieve given formation structures and eliminate the unexpected Zeno behavior. Since the whole protocols are designed according to sampled information at event instants rather than real-time information, these protocols efficiently avoid continuous communications, reduce the bandwidth need of communication, and decrease the energy consuming. The distributed static state feedback edge-based event-triggered protocol or the adaptive one is applicable for the occasions with available states. Different from the state feedback protocols, users can choose the distributed static output feedback edge-based event-triggered protocol or the adaptive one no matter whether agents' states are available or not. It is worth emphasizing that the adaptive state (or output) feedback event-triggered protocol requires no global information of the network topology and can be used in a fully distributed and scalable manner. Finally, numerical examples on formation control are offered to testify the feasibility of the proposed protocols.