The β-skeleton is a mathematical method to construct graphs from a set of points that has been widely applied in the areas of image analysis, machine learning, visual perception, and pattern recognition. In this work, we apply the β-skeleton to study the cosmic web. We use this tool on simulated data to identify the filamentary structures and characterize the statistical properties of the skeleton. We find that the β-skeleton is able to reveal the underlying structures without any parameter fine-tuning. A different degree of sparseness can be obtained by adjusting the value of β. In addition, the statistical properties of the length and direction of the skeleton connections show a clear dependence on the redshift space distortions, volume effect, Alcock–Paczynski effect, and galaxy bias. Our proof-of-concept study shows that the statistical properties of the β-skeleton can be used to probe cosmological parameters and galaxy evolution.