This paper investigates the secure communication in a two-hop cooperative wireless network, where a buffer-aided relay is utilized to forward data from the source to destination, and a passive eavesdropper attempts to intercept data transmission from both the source and relay. Depending on the availability of instantaneous channel state information of the source, two cases of transmission mechanisms, i.e., adaptive-rate transmission and fixed-rate transmission are considered. To enhance the security of the system, novel link selection policies are proposed for both cases to select source-to-relay, relay-to-destination, or no link transmission based on the channels qualities. Closed-form expressions are derived for the end-to-end secrecy outage probability (SOP), secrecy outage capacity (SOC), and exact secrecy throughput (EST), respectively. Furthermore, we prove the condition that EST reaches its maximum, and explore how to minimize the SOP and maximize the SOC by optimizing the link selection parameters. Finally, simulations are conducted to demonstrate the validity of our theoretical performance evaluation, and extensive numerical results are provided to illustrate the efficiency of the proposed link selection polices for the secure communication in two-hop cooperative networks.