the modular graph consists of three clusters of five interconnected nodes. The lattice can be thought of as a grid, wrapping around at its boundary. The random graphs differed between subjects and had no consistent organizational principles besides constituting a single connected component and maintaining the same number of nodes and edges as the other two graphs. (See Methods for formal definitions.) For both the modular and lattice graphs, the equal degree distribution coupled with a random walk leads to uniform pairwise probabilities for all possible transitions from a given node in the graph. Experiment: We ran three experiments, each consisting of two back-to-back stages that differed in which graph and walk type was used to generate the stimulus sequence. The first experiment considered learning on one of three distinct topologies ( modular , lattice , or random ) instantiated as sparse graphs containing only a minority of possible edges between nodes; learning from one of the structured topologies was followed by learning from a fully connected graph structure, in an effort to identify any changes in learning driven by the addition of novel edges. Pragmatically, the experiment was operationalized with a within-subjects design. Specifically, the first stage of the experiment used either a modular , lattice , or random graph to generate a sequence of 1500 stimuli via a random walk on the graph. The second stage of the experiment used a fully connected graph to generate a sequence of 500 stimuli via a random walk on the graph (which amounted to a random stimulus order). With every node connected to every other node (eliminating any informative structure of the input), the fully connected graph allowed a comparison between previously trained edges and novel edges. The second experiment consisted of 1500 trials of a random walk on a modular graph, followed by 500 trials of a Hamiltonian walk on the same graph, allowing us to confirm that learned differences transferred to a different walk type on the same graph structure. The third experiment directly compared learning effects between graph types, accounting for individual variability in baseline reaction times and learning rates using a within-subjects design. Similar to the first experiment, the first stage of the experiment consisted of a sequence of 1500 stimuli via a random walk on either a modular graph, a lattice graph, or a random graph. However, unlike the first experiment, the second stage was another sequence of 1500 stimuli via a random walk on one of the remaining two sparse structured graph types. Analysis: We verified the surprisal effect using all modular graph traversals from stage 1 (Experiment 1). The effect of modifying the graph topology through the addition of novel edges was assessed using a sparse graph followed by a full graph in a between-subjects design (Experiment 1). Our assessment of the sensitivity of the surprisal effect to a switch from a random walk to a Hamiltonian walk was based on Experiment 2. Our comparison of behavioral performance between the sparse graph types (modular, lattice, and random) was based on a within-subjects design (Experiment 3). Finally, our comparison of local and global graph properties was based on data acquired during the random walk traversal of a sparse random graph (stage 1 of Experiments 1 and 3). After determining differences in reaction time by key or key combination (Fig. 1B) (which was then added as a regressor in 6/29