The issue of the low probability of intercept (LPI) radar signal sensing has received considerable attention. Furthermore, the development of military technology further increased demand for it in future electronic warfare (EW). Meanwhile, so far, a systematic understanding of how radar signal detection and recognition technology contributes to EW is still lacking. Therefore, this study aims to contribute to this growing area of research by exploring an automatic method for detecting and identifying radar signals based on visibility graphs (VG), which can extract more network and feature information in the two-dimensional space of VG. In this paper, the signal to be measured is subjected to wavelet noise reduction. Secondly, auto-correlation processing is performed on the signal, we subsequently convert the signal into a VG complex network. Then the average degree and weighted operation of the network are used for signal detection and recognition, respectively. Experiments in the last part indicate that the proposed method provides excellent performance, such as the robustness to noise and the probability of classification, over several state-of-the-art algorithms.