Behaviours across terrorist groups differ based on a variety of factors, such as groups’ resources or objectives. We here show that organizations can also be distinguished by network representations of their operations. We provide evidence in this direction in the frame of a computational methodology organized in two steps, exploiting data on attacks plotted by Al Shabaab, Boko Haram, the Islamic State and the Taliban in the 2013–2018 period. First, we present $\textsf{LabeledSparseStruct}$, a graph embedding approach, to predict the group associated with each operational meta-graph. Second, we introduce $\textsf{SparseStructExplanation}$, an algorithmic explainer based on $\textsf{LabeledSparseStruct}$, that disentangles characterizing features for each organization, enhancing interpretability at the dyadic level. We demonstrate that groups can be discriminated according to the structure and topology of their operational meta-graphs, and that each organization is characterized by the recurrence of specific dyadic interactions among event features.