The complex networks and time series are two classical paradigms to describe the real complex systems. But the complexity of systems determines that we merely can obtain the specific properties of the object given the single paradigm. To address this problem, recently transformation between complex networks and time series becomes promising research. People begin to pay much attention to their internal relationship. Inspired by the previous work, we emphasize the theoretical foundation of equivalent transformation between complex networks and time series to ensure the consistency of dynamics of complex system during transformation, thereby providing theoretical evidences for their reciprocal characterization. Based on that, we confirm and quantify the corresponding relationship between both counterparts and provide characterization methods for their integrated application in practice to comprehensively understand complex systems from the dual perspectives of complex networks and time series.