In this paper, we propose the Liquid-Graph Time- constant (LGTC) network, a continuous graph neural network (GNN) model for control of multi-agent systems based on the recent Liquid Time Constant (LTC) network. We analyse its stability leveraging contraction analysis and propose a closed- form model that preserves the model contraction rate and does not require solving an ODE at each iteration. Compared to discrete models like Graph Gated Neural Networks (GGNNs), the higher expressivity of the proposed model guarantees remarkable performance while reducing the large amount of communicated variables normally required by GNNs. We evaluate our model on a distributed multi-agent control case study (flocking) taking into account variable communication range and scalability under non-instantaneous communication