We calculate both positive and negative price volatilities based on Realized Semi-variance (RS) in major economies’ carbon and energy markets with daily data from 1 July 2013 to 31 May 2023. Subsequently, we construct a network using the Elastic-Net-VAR model to analyze the contagion of price volatilities and examine how shocks affect the connectedness between these markets’ price volatilities using Local Projection. The following findings are presented: (1) There exists a robust correlation between carbon price volatilities and energy price volatilities, with time-varying overall network connectedness ranging from 21.54% to 83.34%. (2) Carbon markets primarily act as recipients of price volatilities, while energy markets serve as initiators. (3) The spillover effects and inflow of negative price volatilities are more pronounced compared to those of positive price volatilities. This is attributed to the fact that declining prices often indicate a market downturn, leading to the easy dissemination of adverse news across interconnected markets. Concurrently, increasing fragility diminishes its resilience against risks. (4) Shocks have a significant influence on the connectedness between carbon prices and energy prices, with different mechanisms at play under different shocks. The COVID-19 pandemic has increased the connectedness between carbon markets and energy markets primarily through common exposure mechanisms. Conversely, geopolitical risks reduce network connectedness by decreasing price complementarity.