  Causality can be described in terms of a structural causal model (SCM) that
carries information on the variables of interest and their mechanistic
relations. For most processes of interest the underlying SCM will only be
partially observable, thus causal inference tries leveraging the exposed. Graph
neural networks (GNN) as universal approximators on structured input pose a
viable candidate for causal learning, suggesting a tighter integration with
SCM. To this effect we present a theoretical analysis from first principles
that establishes a more general view on neural-causal models, revealing several
novel connections between GNN and SCM. We establish a new model class for
GNN-based causal inference that is necessary and sufficient for causal effect
identification. Our empirical illustration on simulations and standard
benchmarks validate our theoretical proofs.
