In this paper, we study the connectedness among 32 energy firms listed in the United States from January 2014 to November 2022. Specifically, we construct a new linear model based on Diebold and Yilmaz's (2012, 2014) approach and Granger causality to estimate the correlation between firms. In addition, we construct a multilayer network containing information on returns, volatilities and extreme risks and measure the network's topological properties from static and dynamic perspectives, respectively. Our empirical results suggest that multilayer networks can be of great use in understanding the relationships among energy firm stocks. Some interesting points include: the oil & gas sector dominates the energy sector; we should focus more on firms with large market capitalization, which are usually strong influence points in the network; the volatility layer is more connected than the return and risk layers; and the impact of the COVID-19 on energy firms is broader and more profound than that of Brexit, the US shale gas revolution, and the US-China trade war.