Graph Neural Networks (GNNs) have been a latest hot research topic in data science, due to the fact that they use the ubiquitous data structure graphs as the underlying elements for constructing and training neural networks. In a GNN, each node has numerous features associated with it. The entire task (for example, classification, or clustering) utilizes the features of the nodes to make decisions, at node level or graph level. In this paper, (1) we extend the feature selection algorithm presented in via Gumbel Softmax to GNNs. We conduct a series of experiments on our feature selection algorithms, using various benchmark datasets: Cora, Citeseer and Pubmed. (2) We implement a mechanism to rank the extracted features. We demonstrate the effectiveness of our algorithms, for both feature selection and ranking. For the Cora dataset, (1) we use the algorithm to select 225 features out of 1433 features. Our experimental results demonstrate their effectiveness for the same classification problem. (2) We extract features such that they are linear combinations of the original features, where the coefficients for each extracted features are non-negative and sum up to one. We propose an algorithm to rank the extracted features in the sense that when using them for the same classification problem, the accuracy goes down gradually for the extracted features within the rank 1 - 50, 51 - 100, 100 - 150, and 151 - 200.