Two-dimensional regular theoretical units that give a negative Poisson’s ratio (NPR) are well documented and well understood. Predicted mechanical properties resulting from these models are reasonably accurate in two dimensions but fall down when used for heterogeneous real-world materials. Manufacturing processes are seldom perfect and some measure of heterogeneity is therefore required to account for the deviations from the regular unit cells in this real-life situation. Analysis of heterogeneous materials in three dimensions is a formidable problem; we must first understand heterogeneity in two dimensions. This paper approaches the problem of finding a link between heterogeneous networks and its material properties from a new angle. Existing optimisation tools are used to create random two-dimensional topologies that display NPR, and the disorder in the structure and its relationship with NPR is investigated.