Can you hear the shape of a graph? It turns out graphs have *spectra*, which can be computed by representing the graph as a matrix, and computing the eigenvalues.

In this example, we compute the normalised Laplacian matrix for a given graph, then map its eigenvalues onto two octaves: *0* becomes *440 Hz* (*A*), *1* becomes *880 Hz* (*A* again), and finally, *2* becomes *1760 Hz*.

To add a new vertex, first select the vertex you want to connect it to. Then **shift-click** (ctrl-click or alt-click will also work). You can shift-click on an existing vertex to connect it to a selected vertex.

To delete a vertex, press delete or backspace.

Do you notice any relationship between symmetry in the graph and the harmoniousness of the chord?

- I was inspired by Can you hear the shape of a graph?, found via Shubhendu Trivedi.
- It turns out this was originally developed by Robert Ellis and he has a more extensive description including more sounds!
- Spectral graph theory on Wikipedia.
- Graph spectrum on MathWorld.

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© Jason Davies 2012.