Pulmonary tuberculosis (TB) is still an important cause of death worldwide, even after being almost eradicated 40 years ago. Early identification of TB in computed tomography (CT) scans can influence therapeutical decisions, thus improving patient outcome. In this paper, a graph model of the lungs is proposed for the classification of TB types using local texture features in thorax CT scans of TB patients. Based on lung morphology, an automatic patient-specific lung field parcellation was initially computed. Local visual features were then extracted from each region and were used to build a personalized lung graph model. A new graph-based patient descriptor enables comparisons between lung graphs with a different number of nodes and edges, encoding the distribution of several node measures from graph theory. The proposed model was trained and tested on a public dataset of 1,513 CT scans of 994 TB patients. The evaluation was performed on data from a scientific challenge together with 39 participant algorithms, obtaining the best unweighted Cohen kappa coefficient of 0.24 in a 5-class setup with 505 test CTs. Even though each lung graph has a unique structure, the proposed method was able to identify key texture changes associated with the different manifestations of TB.