Preterm births have been associated with altered neurological development for neonatal infants, this has been implicated in certain neurodevelopmental conditions in later life. Advances in brain imaging methods, such as Magnetic Resonance Imaging, have allowed for the analysis of physical connectivity of brain matter in infants shortly after birth. However, commonly used methods of investigating such data rely on a brain network analysis, traditionally based on graph-theoretical approaches, which may fail to capture complex patterns involving both local and global network structures and spatial information. Furthermore, many previous studies of infant brain data rely on a priori selection of specific graph connectivity measures. We propose employing machine learning models such as logistic regression and Graph Neural Networks to provide a data-driven approach for classifying preterm and term brain networks at birth. We utilize fuzzy logic, and explainability methods including Shapley Additive Explanations to identify influential regions and connections in decision making. In our analysis, brain regions are represented as spatially embedded nodes, with edges representing strength of structural connections between areas. Using this setup, our model achieves a binary classification accuracy of 88.57%. This performance is further enhanced using a fuzzy boundary between preterm and term classes, achieving an accuracy of 96.19%. This demonstrates that the model can be assisted particularly by adding context to 'near-term' born infant cases. These analyses highlight important connections, and key nodes including deep brain structures which are broadly consistent with biological literature.