  Loop Quantum Gravity provides a natural truncation of the infinite degrees of
freedom of gravity, obtained by studying the theory on a given finite graph. We
review this procedure and we present the construction of the canonical theory
on a simple graph, formed by only two nodes. We review the U(N) framework,
which provides a powerful tool for the canonical study of this model, and a
formulation of the system based on spinors. We consider also the covariant
theory, which permits to derive the model from a more complex formulation,
paying special attention to the cosmological interpretation of the theory.
