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Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited to simple systems such as pendulums and springs or a single rigid body such as a gyroscope or a rigid rotor. Here, we present a Lagrangian graph neural network (LGNN) that can learn the dynamics of articulated rigid bodies by exploiting their topology. We demonstrate the performance of LGNN by learning the dynamics of ropes, chains, and trusses with the bars modeled as rigid bodies. LGNN also exhibits generalizability -- LGNN trained on chains with a few segments exhibits generalizability to simulate a chain with large number of links and arbitrary link length. We also show that the LGNN can simulate unseen hybrid systems including bars and chains, on which they have not been trained on. Specifically, we show that the LGNN can be used to model the dynamics of complex real-world structures such as the stability of tensegrity structures. Finally, we discuss the non-diagonal nature of the mass matrix and its ability to generalize in complex systems.