The analysis of structural and functional neuroimaging data using graph theory has increasingly become a popular approach for visualising and understanding anatomical and functional relationships between different cerebral areas. In this work we applied a network-based approach for brain PET studies using population-based covariance matrices, with the aim to explore topological tracer kinetic differences in cross-sectional investigations. Simulations, test-retest studies and applications to cross-sectional datasets from three different tracers ([18F]FDG, [18F]FDOPA and [11C]SB217045) and more than 400 PET scans were investigated to assess the applicability of the methodology in healthy controls and patients. A validation of statistics, including the assessment of false positive differences in parametric versus permutation testing, was also performed. Results showed good reproducibility and general applicability of the method within the range of experimental settings typical of PET neuroimaging studies, with permutation being the method of choice for the statistical analysis. The use of graph theory for the quantification of [18F]FDG brain PET covariance, including the definition of an entropy metric, proved to be particularly relevant for Alzheimer’s disease, showing an association with the progression of the pathology. This study shows that covariance statistics can be applied to PET neuroimaging data to investigate the topological characteristics of the tracer kinetics and its related targets, although sensitivity to experimental variables, group inhomogeneities and image resolution need to be considered when the method is applied to cross-sectional studies.