Diagnosing Interstitial Lung Diseases (ILD) is a difficult task. It requires experienced chest radiologists that may not be available in less-specialized health centers. Moreover, a correct diagnosis is needed to decide for an appropriate treatment and prognostic. In this paper, we focus on the classification of 3 common subtypes of ILDs: Usual Interstitial Pneumonia (UIP), Non-Specific Interstitial Pneumonia (NSIP) and Chronic Hypersensitivity Pneumonitis (CHP). We propose a graph model of the lungs built from a large dataset. The structure of the graph is inspired from medical knowledge of disease predominance, where the nodes correspond to 24 distinct regions obtained from lateral, anterior-posterior and vertical splits of the images. The adjacency matrix is built from distances between intensity distributions of distinct regions. Graphs models are interpretable and were successfully used in neuroimaging. However, to the best of our knowledge, this is the first attempt to use a graph model of the lungs for classifying ILDs. In the particular case of ILDs, graph methods are relevant for the following reasons. In order to differentiate between the subtypes, not only the types of local patterns of the disease are important but also their anatomical location. Therefore, we hypothesize that the comparison between regional distributions of Hounsfield Unit (HU) values is relevant to discriminate between the considered ILD subtypes. For instance, typical UIP shows a spatial predominance of reticular abnormalities and honeycombing in the peripheral regions of the lung bases. Therefore, we expect a marked difference of HU distributions between the central and peripheral regions of the lung bases. Moreover, the construction of the graph leads to an interpretable patient descriptor. The descriptor led to encouraging area under the Receiver Operating Characteristic (ROC) curve in 0.6-0.8 for one-versus-one classification configurations, which also showed to outperform feature sets based on a simple concatenation of regional HU distributions.