The relationship between Graph Laplacian eigenvectors and LAM.

(A) Fiedler vector (GL eigenvector with the second smallest eigenvalue) for the graph in Schapiro et al. (2013). (B) Fiedler vector for karate-club network. (C) The comparison of pattern overlaps in LAM (α = −0.9) and Fiedler vector for the four-room graph. (D) A schematic diagram showing that pattern overlaps in LAM (α = −0.5) is mostly explained by the combination of multiple GL eigenvectors with small eigenvalues. (E-G) The explained variance ratio in linear regressions of pattern overlaps by various numbers of GL eigenvectors. The color indicates the value of α. In each condition, we plotted the average value of the explained variance ratio of attractors reached from all trigger stimuli. (E) Results from the graph by Schapiro et al. (2013). (F) Results for the karate-club network. (G) Results for the four-room graph.