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Combined positron emission tomography and computed tomography (PET-CT) scans have become a critical tool for the diagnosis, localisation, and staging of most cancers. This has led to a rapid expansion in the volume of PET-CT data that is archived in clinical environments. The ability to search these vast imaging collections has potential clinical applications in evidence-based diagnosis, physician training, and biomedical research that may lead to the discovery of new knowledge. Content-based image retrieval (CBIR) is an image search technique that complements conventional text-based retrieval by the use of image features as search criteria. Graph-based CBIR approaches have been found to be exemplary methods for medical CBIR as they provide the ability to consider disease localisation during the similarity measurement. However, the majority of graph-based CBIR studies have been based on 2D key slice approaches and did not exploit the rich volumetric data that is inherent to modern medical images, such as multi-modal PET-CT. In this paper, we present a graph-based CBIR method that exploits 3D spatial features extracted from volumetric regions of interest (ROIs). We index these features as attributes of a graph representation and use a graph-edit distance to measure the similarity of PET-CT images based on the spatial arrangement of tumours and organs in a 3D space. Our study aims to explore the capability of these graphs in 3D PET-CT CBIR. We show that our method achieves promising precision when retrieving clinical PET-CT images of patients with lung tumours.