This paper introduces a type of graph called 'homeomorphically irreducible tree' (HIT) and explores its analytical and computational aspects in the architecture of radial prison plans. As a theoretical introduction, HITs are first diagrammatically presented using a taxonomy of 20 different radial prisons. Using this analysis, a generative algorithm that transforms plan connectivity to a simple sequential numeric representation is developed. This method is applied as an architectural plan generator that is parametrically explored using graphs as building skeletons with configurable wing typologies. The aim of the paper is to lay the foundation of a new graph-based approach for the morphogenetic study of symmetry in architectural plans.
