Financial markets are complex systems. Network analysis is an innovative method for improving data sharing and knowledge discovery in financial data. Oriented weighted networks were created for the Shanghai Composite, S&P500, DAX30, CAC40, Nikkei225, FTSE100, IBEX35 indexes, for CNY-JPY, EUR-USD, GBP-EUR, RUB-CNY and for cryptocurrency BTC-USD. We considered data since January 6, 2006 to September 6, 2019. The complex networks had a similar structure for both types of markets, which was divided into the central part (core) and the outer one (loops). The emergence of such a structure reflects the fact that, for the most part, the stock and currency markets develop around some significant state of volatility, but occasionally anomalies occur when the states of volatility deviate from the core. Comparing the topology of evolutionary networks and the differences found for the stock and currency markets networks, we can conclude that stock markets are characterized by a greater variety of volatility patterns than currency ones. At the same time, the cryptocurrency market network showed a special mechanism of volatility evolution compared to the currency and stock market networks.