In recent years, graph neural networks (GNNs) have become the de facto tool for performing machine learning tasks on graphs. Most GNNs belong to the family of message passing neural networks (MPNNs). These models employ an iterative neighborhood aggregation scheme to update vertex representations. Then, to compute vector representations of graphs, they aggregate the representations of the vertices using some permutation invariant function. One would expect the hidden layers of a GNN to be composed of parameters that take the form of graphs. However, this is not the case for MPNNs since their update procedure is parameterized by fully-connected layers. In this paper, we propose a more intuitive and transparent architecture for graph-structured data, so-called Random Walk Graph Neural Network (RWNN). The first layer of the model consists of a number of trainable ``hidden graphs'' which are compared against the input graphs using a random walk kernel to produce graph representations. These representations are then passed on to a fully-connected neural network which produces the output. The employed random walk kernel is differentiable, and therefore, the proposed model is end-to-end trainable. We demonstrate the model's transparency on synthetic datasets. Furthermore, we empirically evaluate the model on graph classification datasets and show that it achieves competitive performance.