In high-energy particle collisions, the primary collision products usually decay further resulting in tree-like, hierarchical structures with a priori unknown multiplicity. At the stable-particle level all decay products of a collision form permutation invariant sets of final state objects. The analogy to mathematical graphs gives rise to the idea that graph neural networks (GNNs), which naturally resemble these properties, should be best-suited to address many tasks related to high-energy particle physics. In this paper we describe a benchmark test of a typical GNN against neural networks of the well-established deep fully-connected feed-forward architecture. We aim at performing this comparison maximally unbiased in terms of nodes, hidden layers, or trainable parameters of the neural networks under study. As physics case we use the classification of the final state X produced in association with top quark-antiquark pairs in proton-proton collisions at the Large Hadron Collider at CERN, where X stands for a bottom quark-antiquark pair produced either non-resonantly or through the decay of an intermediately produced Z or Higgs boson.
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