This paper presents an automated and effective method for detecting 3D edges and tracing feature lines from 3D-point clouds. This method is named Analysis of Geometric Properties of Neighborhoods (AGPN), and it includes two main steps: edge detection and feature line tracing. In the edge detection step, AGPN analyzes geometric properties of each query point's neighborhood, and then combines RANdom SAmple Consensus (RANSAC) and angular gap metric to detect edges. In the feature line tracing step, feature lines are traced by a hybrid method based on region growing and model fitting in the detected edges. Our approach is experimentally validated on complex man-made objects and large-scale urban scenes with millions of points. Comparative studies with state-of-the-art methods demonstrate that our method obtains a promising, reliable, and high performance in detecting edges and tracing feature lines in 3D-point clouds. Moreover, AGPN is insensitive to the point density of the input data.