Amid the deep integration of energy and finance, the stock price linkage of energy companies exhibits complex network characteristics. From the perspective of risk and return, this study constructs minimum spanning tree networks of returns, volatility, and investor sentiment for Chinese new energy and traditional energy companies, identifying the impact of COVID-19 and the dual-carbon policy on these networks. The empirical results show: (1) The sentiment network has the highest transmission efficiency and easily transmits between the two types of companies, while the return network has the lowest transmission efficiency and primarily transmits within the same type of companies. (2) During the COVID-19 pandemic, the transmission efficiency of all networks increased. (3) After the dual-carbon policy, the correlation between the two types of companies weakened, and the similarity between the return, volatility, and sentiment networks increased. This study helps regulators monitor systemically important companies and guides investors in risk management based on multidimensional network characteristics.