As the advantage of lower latency and energy consumption, fog computing has been seen as an important enabler to meet the harsh requirements of Industrial Internet of Things (IIoT), which links multiple industrial wireless sensors (IWSs) with limited energy and computing ability, via offloading computation and analysis tasks to Fog Access Points (F-APs). However, F-APs often transmit all information-packages of IWS in traditional methods, making long delay in transmitting massive data-sets. To overcome this issue, we propose a link-aware IWSs sleeping scheme via graph signal sampling and reconstruction strategy in a local IIoT network scenario with multiple IWSs and one F-AP, aiming at prolonging the IIoT network lifetime and spreading out maintenance time. The simulation results demonstrate the effectiveness of the proposed scheme from the perspective of reconstruction performance, robustness on classical graph structures and the graph cutoff frequency bound. It can be seen that the proposed scheme could reduce the subsampling rate while keeping the reconstruction convergence rate compared with the baseline algorithm.