Organized into a global network of critical infrastructures, the oil & gas industry remains to this day the main energy contributor to the world's economy. Severe accidents occasionally occur resulting in fatalities and disruption. We build an oil & gas accident graph based on more than a thousand severe accidents for the period 1970-2016 recorded for refineries, tankers, and gas networks in the authoritative ENergy-related Severe Accident Database (ENSAD). We explore the distribution of potential chains-of-events leading to severe accidents by combining graph theory, Markov analysis and catastrophe dynamics. Using centrality measures, we first verify that human error is consistently the main source of accidents and that explosion, fire, toxic release, and element rupture are the principal sinks, but also the main catalysts for accident amplification. Second, we quantify the space of possible chains-of-events using the concept of fundamental matrix and rank them by defining a likelihood-based importance measure γ. We find that chains of up to five events can play a significant role in severe accidents, consisting of feedback loops of the aforementioned events but also of secondary events not directly identifiable from graph topology and yet participating in the most likely chains-of-events.