Cognitive maps have been proposed as an essential relational structure for human memory and thought (Tolman, 1948; Constantinescu et al., 2016). In this format, remembered entities are embedded in space and their relationships are encoded via concrete angles and Euclidean distances. Although much of higher human cognition may be spatial, cognitive maps are not the only possible relational structure. With a behavioral experiment we aim to challenge the extent of the cognitive map hypothesis and to investigate when and how humans represent knowledge via the relational structure of cognitive graphs (Kuipers, 1982; Garvert et al., 2017). In this format, entities and their relationships are represented via abstract, topological connectivity. In contrast to spatial structure, topological connectivity is invariant under continuous transformations, and as a result, angles and Euclidean distances are meaningless. In our experiment, we let participants learn a fixed graph structure that is presented on a map-like 2D surface (i.e. the monitor), but whose presentation varies methodically over learning trials for five different groups of participants. For group 1, we keep the presentation entirely static. When probing the learned graph representations, we expect to find that participants are strongly influenced by the Euclidean spatial presentation. For groups 2, 3 and 4, we vary the presentation in different ways: we rotate the graph structure around the surface's centre, we vary the distances between embedded objects (akin to a scaling of the graph), and we vary the angles of edges in-between them. In general, we believe that the more we vary the presentation, the less we expect to find an effect of the influence of Euclidean space. Finally, for group 5, we vary the graph presentation randomly and without constraints. Thereby, we expect to eliminate the spatial influence entirely. There is the possibility however that space can never be fully eliminated and in which case it could be an intrinsic scaffold of human cognition. Here, we present the data of this experiment for the first time. Since it explicitly tests a computational framework about structure in thought, that has given rise to many theoretical ideas and computational models (Stachenfeld et al., 2017; Whittington et al. 2020), we believe the results to be of significant interest to computational neuroscience.