This article presents a novel graph–model approach encoding the relations between the perfusion in several regions of the lung extracted from a geometry–based atlas. Unlike previous approaches that individually analyze regions of the lungs, our method evaluates the entire pulmonary circulatory network for the classification of patients with pulmonary embolism and pulmonary hypertension. An undirected weighted graph with fixed structure is used to encode the network of intensity distributions in Dual Energy Computed Tomography (DECT) images. Results show that the graph–model presented is capable of characterizing a DECT dataset of 30 patients affected with disease and 26 healthy patients, achieving a discrimination accuracy from 0.77 to 0.87 and an AUC between 0.73 and 0.86. This fully automatic graph–model of the lungs constitutes a novel and effective approach for exploring the various patterns of pulmonary perfusion of healthy and diseased patients.