A method, apparatus, system, article of manufacture, and computer program product provide the ability to utilize a degree of freedom (DOF) for a construction. In a preparation phase, a graph structure is constructed from a construction model that transforms construction primitives into graph primitives. In a search phase, all compact sub-graphs of the graph structure are identified. In a counting phase, a DOF is calculated for each compact sub-graph and adjusted based on interactions between the compact sub-graphs. In an internal DOF searching phase, an internal DOF is computed for each compact sub-graph and used to determine and solve overconstrained sub-graphs. A determination regarding whether a structure of the construction model can be modified based on the DOF and internal DOF is output.