Title: NODE-SELECT: A FLEXIBLE GRAPH NEURAL NETWORK BASED ON REALISTIC PROPAGATION SCHEME. Abstract: While there exists a wide variety of graph neural networks (GNN) for node classification, only a minority of them adopt effective mechanisms to propagate the nodes' information with respect to these nodes' global importance. Additionally, two very important challenges that still significantly affect graph neural networks are the over-fitting and over-smoothing issues. Essentially, both issues cause poor generalization of the model and much poorer node classification performance. In this paper we propose the NODE-SELECT graph neural network (NSGNN): a novel and flexible graph neural network that uses subsetting filters to learn the contribution from the nodes selected to share their information. For the selected nodes, the way their learned information propagates resembles that of actual networks of the real world; where only a subset of nodes simultaneously share information. With the ability to manipulate the message passing operations through the use of numerous ensembled filters, our NODE-SELECT graph neural network is able to address the over-fitting problem and by-pass the over-smoothing challenge for graph neural networks. Furthermore, we also propose an efficient and informative measure named MICS to quantify the over-smoothing problem. Our NODE-SELECT achieved or matched state-of-the art results in a number of transductive experiments over different benchmark datasets.