Title: Graph-based motion planning networks. Abstract: Differentiable planning network architecture has shown to be powerful in solving transfer planning tasks while possesses a simple end-to-end training feature. Many great planning architectures that have been proposed later in literature are inspired by this design principle in which a recursive network architecture is applied to emulate backup operations of a value  iteration algorithm. However existing frame-works can only learn and plan effectively on domains with a lattice structure, i.e. regular graphs embedded in a certain Euclidean space. In this paper, we propose a general planning network, called Graph-based Motion Planning Networks (GrMPN), that will be able to i) learn and plan on general irregular graphs, hence ii) render existing planning network architectures special cases. The proposed GrMPN framework is invariant to task graph permutation, i.e. graph isormophism. As a result, GrMPN possesses the generalization strength and data-efficiency ability. We demonstrate the performance of the proposed GrMPN method against other baselines on three domains ranging from 2D mazes (regular graph), path planning on irregular graphs, and motion planning (an irregular graph of robot configurations).