Robust representation of the spatial arrangement of topological features.

Recent work has shown that people are sensitive to coarse differences in network topology, including network features like "holes," "crosses," and "T-junctions." Even children as young as 4 years old will readily distinguish between items that differ slightly in their network topology. But how robust is this sensitivity? Here, we evaluate whether people are not only sensitive to differences in the presence or absence of certain topological features, but also to their exact spatial arrangement. In a first experiment, we show that people distinguish figures which possess all the same topological features as other figures in a set if the features differ in spatial arrangement. In a second experiment, we show that people also match figures based on exact spatial arrangement. Finally, we show that memory encodes the correct relational structure of the figures: People are more likely to falsely indicate having seen an item if it shared the precise arrangement of topological features of other items they had seen (compared to a closely matched item which had the same features arranged in a different way). Combined, these results bolster the theory that people intuitively appreciate the precise spatial arrangement of topological features.