This paper presents an extension of the graphic-statics-based framework called Combinatorial Equilibrium Modelling (CEM). CEM allows for the generation of topologically and combinatorially different spatial equilibrium solutions in the early explorative design phase. In addition to the form and the force diagrams, CEM introduces a topological diagram, which enables the possibility to easily adjust the connectivity of the structure, the combinatorial state (tension-compression) as well as the static action (product of each element’s length and its corresponding force magnitude) of its inner forces. Thanks to its planarity, the topological diagram is always visually readable, comprehensible and easy to control, even in case of complex spatial structures. This innovative approach has the potential to find novel spatial networks in which the intrinsic structural properties can be controlled by the designer with simple visual operations.