2D Graph Neural Network Message Passing

Every Graph Neural Network layer runs the same core operation: each node collects and aggregates the feature vectors of its neighbors, then updates its own vector from that aggregate. This 2D simulator draws a graph natively in the plane (a 2D k-nearest-neighbor topology over randomly scattered points, not a projected 3D layout) and, side by side, plots every node's 3-dimensional feature vector as a point in embedding space — its first two components as (x, y), its third as brightness. Stepping through sum, mean, or the symmetric-normalized rule from Kipf & Welling's GCN animates pulses along the graph edges on the left while the point cloud on the right visibly contracts toward its centroid, making the well-known over-smoothing effect directly observable as geometry collapsing in feature space rather than just colors converging on a 3D mesh. Live readouts track the hop count, Dirichlet energy, and embedding variance.