Title: P^2IR: Universal Deep Node Representation via Partial Permutation Invariant Set Functions. Abstract: Graph node representation learning is a central problem in social network analysis, aiming to learn the vector representation for each node in a graph. The key problem is how to model the dependence  of each node to its neighbor nodes since the neighborhood can uniquely characterize a graph. Most existing approaches rely on defining the specific neighborhood dependence as the computation mechanism of representations, which may exclude important subtle structures within the graph and dependence among neighbors. Instead, we propose a novel graph node embedding method (namely P^2IR) via developing a novel notion, namely partial permutation invariant set function} to learn those subtle structures. Our method can 1) learn an arbitrary form of the representation function from the neighborhood, without losing any potential dependence structures, 2) automatically decide the significance of neighbors at different distances, and 3) be applicable to both homogeneous and heterogeneous graph embedding, which may contain multiple types of nodes. Theoretical guarantee for the representation capability of our method has been proved for general homogeneous and heterogeneous graphs. Evaluation results on benchmark data sets show that the proposed P^IR outperforms the state-of-the-art approaches on producing node vectors for classification tasks.