Graph Laplacian explorer

Click the canvas to place points from two categories, build a k-nearest-neighbor graph, and see where the Laplacian of the category indicator is nonzero.

Hover a point to read its value. Keys 1 and 2 switch category.

Place points

Category A Category B

Neighbor graph

Neighbors (k)

Show edges

Place at least two points, then generate the graph.

Color shows |Lf|

Points: 0
Edges: –
Largest |Lf|: –
Points with Lf ≠ 0: –

The Laplacian is L = D − W. W marks the neighbor edges, and a pair is connected if either point lists the other among its k nearest. D holds each point’s degree.

The function f is 1 on category A and 0 on category B. Entry i of Lf is the sum over neighbors j of f_i − f_j, so |Lf|_i counts the neighbors of point i in the other category. Swapping A and B gives the same colors.