Hamiltonian walk (Fig. 2D; t ( 57 ) = 10 . 089 , p < 0 . 001, Pearson’s correlation coefficient r = 0 . 8, 95% confidence interval: 0.69 to 0.88), suggesting a diminished yet persistent effect of topological edge role after eliminating local repetitions. We verified that this result was not the result of idiosyncrasies in assignment of motor actions to nodes by performing a permutation test where the identity of cross-cluster edges was randomly assigned (see Supplementary Fig. 3). 

While the cross-cluster surprisal effect is a useful measure of how well a modular graph is being learned, it is not a measure that generalizes to non-modular structures. To quantitatively examine the learnability of graph structure across many graph topologies, it would be useful to develop a generalizable measure of the learnability of single transitions from one button press to another. In developing such a measure, it is important to note that two potential explanations exist for improvement in response to a given target: (i) improvement is node-dependent (for all edges leading to that node), or (ii) improvement is edge-dependent, with the rate of improvement depending on the preceding node. Notably, the inclusion of additional edges (with the same set of nodes) in stage 2 of Experiment 1 led to a large increase in mean reaction time (Fig. 3A). To verify that subjects had learned the edges versus nodes of the graph, we examined stage 2 of Experiment 1: when subjects were shown (and asked to respond to) a sequence of stimuli drawn from a fully connected graph. We labeled each edge as either previously learned or not previously learned, based on the respective motor action assigned to the endpoint nodes and whether the edge (sequence of motor actions) was present in the graph learned by that subject in the first stage. We then estimated learner sensitivity to new edges as measured by a change in reaction time, which we referred to as the novel edge effect (see Methods). Using a mixed effects model, we found that subjects were significantly slower when responding to edges that had not previously been seen, with an expected increase of 25.5 ms (linear mixed effects model; Supplementary Table 4; t ( 131 ) = 4 . 35 , p < 0 . 001, 95% confidence interval: 14.01 to 37.0). This finding supports the notion that subjects learn single edges in a graph. However, altering the number of edges in the graph decreases predictability of transitions from a single node. 

While subjects were faster on previously seen edges, this difference in reaction time could be attributable to improvements in compound motor movements, rather than to the learning of any higher-order structure. We therefore asked whether reaction time improvements for sequences generated by each graph type might modulate this novel edge effect. In other words, was it the case that subjects with greater sensitivity to graph structure would be more affected by disruptions to it? Further, might this association between learning measures differ by graph type? We estimated each subject’s learning rate$^{27}$, and we also estimated the novel edge effect for each subject. We found that faster learners showed a significantly greater novel edge effect in the second stage of the experiment than slower learners (Fig. 3B; t ( 107 ) = 3 . 79 , p < 0 . 001 Pearson’s correlation coefficient r = 0 . 34, 95% confidence interval: 0.17 to 0.50). When subdivided by graph type (Fig. 3C), this effect was significant for the 

