Abstract: The authors propose in this article a conceptually new methodological approach to the analysis of financial time series, which is used along with other methods for the study of financial markets’ complexity. The core idea of this approach is construction of new measures of market’s dynamic complexity on the basis of transforming the time series of financial data to «complex networks» based on the principle of recurrence of states in system’s phase trajectory. Then for built network is calculated a wide set of measures that represent a variety of spectral and topological characteristics of the network. The realization of «sliding window» algorithm allows tracing the graphodynamics of the complex system. It’s expedient to use as an indicator-harbinger of changes in the financial markets such from selected measures of complexity, which demonstrates a characteristic behavior in time, coinciding with certain critical market changes. Experimental studies of complex networks, constructed in the framework of proposed methodological approach, confirmed their adequacy and high ability to predict the crisis phenomena in the stock markets.