The specific emitter identification (SEI) technique determines the unique emitter of a given signal by using some external feature measurements of the signal. It has recently attracted a great deal of attention because many applications can benefit from it. This work addresses the SEI problem using two methods, namely, the normalized visibility graph entropy (NVGE) and the normalized horizontal visibility graph entropy (NHVGE) based on treating emitters as nonlinear dynamical systems. Firstly, the visibility graph (VG) and the horizontal visibility graph (HVG) are used to convert the instantaneous amplitude, phase and frequency of received signals into graphs. Then, based on the information captured by the VG and the HVG, the normalized Shannon entropy (NSE) calculated from the corresponding degree distributions are utilized as the rf fingerprint. Finally, four emitters from the same manufacturer are utilized to evaluate the performance of the two methods. Experimental results demonstrate that both the NHVGE-based method and NVGE-based method are quite effective and they perform much better than the method based on the normalized permutation entropy (NPE) in the case of a small amount of data. The NVGE-based method performs better than the NHVGE-based method since the VG can extract more information than the HVG does. Moreover, our methods do not distinguish between the transient signal and the steady-state signal, making it practical.