We study the problem of learning graph dynamics of deformable objects that generalizes to unknown physical properties. Our key insight is to leverage a latent representation of elastic physical properties of cloth-like deformable objects that can be extracted, for example, from a pulling interaction. In this paper we propose EDO-Net (Elastic Deformable Object - Net), a model of graph dynamics trained on a large variety of samples with different elastic properties that does not rely on ground-truth labels of the properties. EDO-Net jointly learns an adaptation module, and a forward-dynamics module. The former is responsible for extracting a latent representation of the physical properties of the object, while the latter 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, 2) transferring the learned representation to new downstream tasks.