In this paper, a novel analysis method based on recurrence networks is proposed to characterize the evolution of dynamical systems. Through phase space reconstruction, a time series was transformed into a high-dimensional recurrence network and a corresponding low-dimensional recurrence network, respectively. Then, two appropriate statistics, the correlation coefficient of node degrees (CCND) and the edge similarity, were proposed to unravel the evolution properties of the considered signal. Through the investigation of the time series with distinct dynamics, different patterns in the decline rate of the CCND at different network dimensions were observed. Interestingly, an exponential scaling emerged in the CCND analysis for the chaotic time series. Moreover, it was demonstrated that the edge similarity can further characterize dynamical systems and provide detailed information on the studied time series. A method based on the fluctuation of edge similarities for neighboring edge groups was proposed to determine the number of groups that the edges should be partitioned into. Through the analysis of chaotic series corrupted by noise, it was demonstrated that both the CCND and edge similarity derived from different time series are robust under additive noise. Finally, the application of the proposed method to ventricular time series showed its effectiveness in differentiating healthy subjects from ventricular tachycardia (VT) patients.