The Music of Graphs

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?

Graph Spectrum

Laplacian Matrix

Credits and Further Reading

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