In this study, we examine the asymmetric short- and long-run spillover among commodities using realized variances and realized semivariances calculated through 5-min trading data of commodity futures. In doing so, we apply time and frequency domain generalized error variance decomposition approaches and build a network of commodity connectedness. Our findings indicate low inter-group connectedness, distinct group clustering, and high intragroup network-based connectedness in realized volatilities of sample commodities. We find more pronounced inter- and intra-group volatility connectedness for negative realized volatilities than positive ones. Besides, we show that volatility connectedness is a long-run phenomenon. Additionally, the time-varying net directional spillover connectedness reveals that the bad volatility connectedness dictates the good volatility connectedness for the total sample as well as for various frequency domains, both in terms of magnitude and length of time. The implications for investors and policymakers are discussed.