An international push to decarbonize economies has initiated a major transition in the global energy system and has begun to disrupt the intricate network of energy trade. As trade patterns begin to reconfigure, it is important that policy makers understand how vulnerabilities of the existing network may present obstacles to a smooth energy transition. We analyze the topology of the global energy trade network in aggregate, for various energy commodities, and for individual countries. Using the network science technique of triad analysis, which examines the prevalence of 3-node subnetworks in a target network, we calculate triad significance profiles for each network. We then analyze whether various triads are under- or over-represented in our networks and find that triads associated with stability appear more frequently than expected, whereas triads associated with conflict appear less frequently than expected. We further find that the global energy trade network is quite robust against disruptions, maintaining its topological characteristics even after random removal of 80% of the network’s nodes. However, when analyzing individual countries, we find that some exhibit a high prevalence of unstable triads or a low prevalence of stabilizing triads, suggesting that vulnerabilities in global energy trade are more pronounced in some countries than others.