Graph was one of random/lattice/modular, and Trial was the sequential trial number (1 to 1500). We verified experimentally that log ( Trial ) provided a substantially better fit than Trial (See Supplementary Fig. 9). The log transformation served to increase the normality of the data, although formal testing of the degree of normality was not performed. Surprisal Effect: One measure reflective of meso-scale graph structure is the surprisal effect , defined as an increase in reaction time when transitioning to a new cluster as compared to any previous within-cluster reaction times$^{4}$. To measure this effect in our task, we fit a linear mixed effects model of the form RT ∼ log ( Trial ) ∗ EdgeType + Target +( 1 + log ( Trial ) ∗ EdgeType | Subject ) to data acquired during the first stage of the experiment on the modular graph where RT is reaction time, and where EdgeType indicated whether an edge was within or between clusters. From this model, we examined the model coefficient for EdgeType . Surprisal Transfer: We fit the surprisal effect model separately to the stage 1 (random walk) and stage 2 (Hamiltonian walk) data from Experiment 2. We estimated the per-subject effect of EdgeType as a measure of surprisal, and additionally examined the Pearson correlation coefficient between each subject’s surprisal effect in stage 1 versus surprisal effect in stage 2. Novel Edge Effect: Next, we sought to examine whether subjects were specifically improving their performance at transitions present in the graph and therefore sensitive to violations of the learned structure of the graph. We defined a LearnedEdge variable for all edges in stage 2 that was true if an edge between the set of finger combinations had been present in the first stage, and false otherwise. We then computed a novel edge effect measure as the coefficient for learned versus unlearned edges in a linear mixed effects model fit to the fully connected graph data using RT ∼ log ( Trial ) ∗ Graph ∗ LearnedEdge + Target +( 1 + log ( Trial ) ∗ LearnedEdge | Subject ) . Graph Effects: In the third experiment, we investigated whether differences in meso-scale structure affected learnability by quantifying reaction time differences due to graph type. Since not all subjects were exposed to all graph types, we split the data into three groups based on exposure: modular/lattice, random/modular, and random/lattice, with each group roughly split by which graph was used for the first stage versus for the second stage. We fit a linear mixed effects model to each of the three data subsets, in order to estimate whether graph type was a significant effect in each model: RT ∼ log ( Trial ) ∗ Graph ∗ Stage + Target +( 1 + log ( Trial ) ∗ Graph | Subject ) , where Trial varied between 1 and 1500, Graph was the current graph of the two graphs that the subject saw, and Stage corresponded to either the first stage or the second stage. Node Effects: After determining the effect of graph type, we finally turned to quantifying the impact of node-level statistics, or those that could explain reaction time differences within a single graph. We examined several traditional graph metrics: degree, clustering coefficient, node betweenness centrality, and edge betweenness centrality. The degree is defined as the 24/29