Detecting salient objects in complicated scenarios is a challenging problem. Except for semantic features from the RGB image, spatial information from the depth image also provides sufficient cues about the object. Therefore, it is crucial to rationally integrate RGB and depth features for the RGB-D salient object detection task. Most existing RGB-D saliency detectors modulate RGB semantic features with absolution depth values. However, they ignore the appearance contrast and structure knowledge indicated by relative depth values between pixels. In this work, we propose a depth-induced network (DIN) for RGB-D salient object detection, to take full advantage of both absolute and relative depth information, and further, enforce the in-depth fusion of the RGB-D cross-modalities. Specifically, an absolute depth-induced module (ADIM) is proposed, to hierarchically integrate absolute depth values and RGB features, to allow the interaction between the appearance and structural information in the encoding stage. A relative depth-induced module (RDIM) is designed, to capture detailed saliency cues, by exploring contrastive and structural information from relative depth values in the decoding stage. By combining the ADIM and RDIM, we can accurately locate salient objects with clear boundaries, even from complex scenes. The proposed DIN is a lightweight network, and the model size is much smaller than that of state-of-the-art algorithms. Extensive experiments on six challenging benchmarks, show that our method outperforms most existing RGB-D salient object detection models.