In recent years, there has been a growing interest in mapping data from different domains to graph structures. Among others, neural network models such as the multi-layer perceptron (MLP) can be modeled as graphs. In fact, MLPs can be represented as directed acyclic graphs. Graph neural networks (GNNs) have recently become the standard tool for performing machine learning tasks on graphs. In this work, we show that an MLP is equivalent to an asynchronous message passing GNN model which operates on the MLP's graph representation. We then propose a new machine learning model for tabular data, the so-called Graph Neural Machine (GNM), which replaces the MLP's directed acyclic graph with a nearly complete graph and which employs a synchronous message passing scheme. We show that a single GNM model can simulate multiple MLP models. We evaluate the proposed model in several classification and regression datasets. In most cases, the GNM model outperforms the MLP architecture.