Monitoring the states of network links is essential to detect network outages and improve Internet reliability. Currently, existing work detects network outages by monitoring all the links, which requires thousands of probes and large-scale measurements, resulting in high resource occupancy and cost. To solve this problem, this paper proposes the KL-Dection approach, which detects network outages via key links instead of all links. Firstly, we recognize the key links based on flow density, degree centrality, and probe-distance centrality. Next, based on the recognized key links, we give the critical value of their Round-Trip Time (RTT). Then, we detect the network outages by observing whether the RTT of the key link exceeds the critical value. Finally, we leverage two historical events to evaluate our approach, and the results demonstrate that our approach can detect the network outages effectively by only monitoring less than 0.06% of the links in detection area.