Refinement is the part of the hierarchical radiosity algorithm that decides the best subdivision of the scene geometry to meet user goals using minimum resources. The refinement oracle is a central component of the radiosity algorithm, because it affects the computation time and the radiosity computation error. Hierarchical radiosity refinement remains a research topic today because of the variety of the geometric and radiometric configurations encountered: currently there does not exist a universal oracle that works well in all the different scene geometries and lighting configurations. It is therefore highly desirable to develop flexible tools for the generation of appropriate oracles suited to different tasks. In this paper we propose a graph structure for the refinement process and a classification of the elementary problems the oracle can handle during the refinement. This representation clarifies the complex refinement process by reducing it to the composition of simple tools. New refiners can easily be created or modified with a marginal increase of the computation time, and many advantages in terms of automatic checking and performance analysis.