We study the problem of learning graph dynamics of deformable objects which generalize to unknown physical properties. In particular, we leverage a latent representation of elastic physical properties of cloth-like deformable objects which we explore through a pulling interaction. We propose EDO-Net (Elastic Deformable Object - Net), a model trained in a self-supervised fashion on a large variety of samples with different elastic properties. EDO-Net jointly learns an adaptation module, responsible for extracting a latent representation of the physical properties of the object, and a forward-dynamics module, which leverages the latent representation to predict future states of cloth-like objects, represented as graphs. We evaluate EDO-Net both in simulation and real world, assessing its capabilities of: 1) generalizing to unknown physical properties of cloth-like deformable objects, 2) transferring the learned representation to new downstream tasks.