Shows a small graph whose adjacency (A) and degree (D) matrices combine into the Laplacian L = D − A. A pulsing “bridge” edge smoothly turns a disconnected graph into a connected one; the Laplacian eigenvalue bars update in real time to demonstrate that the number of near-zero eigenvalues matches the number of connected components, and that the second-smallest eigenvalue (algebraic connectivity λ1) becomes positive exactly when the graph is connected.
Uses a small (6×6) Laplacian and a lightweight Jacobi iteration to approximate eigenvalues each frame. The bridge edge is treated as a weighted adjacency entry so λ1 lifts smoothly during the animation. All drawing is grid-snapped for a retro blocky look with green-on-black styling.