Spectral gap

For the physical quantity, see Spectral gap (physics).

In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes taken as the smallest non-zero eigenvalue. Various theorems relate this difference to other properties of the system. The spectral gap gets its name from the matrix spectrum, that is, for a matrix, the list of its eigenvalues. It provides insight on diffusion within the graph: corresponding the spectral gap to the smallest non-zero eigenvalue, it is then the mode of the network state that shows the slowest exponential decay over time.

See also

• Cheeger constant (graph theory)
• Cheeger constant (Riemannian geometry)
• Eigengap
• Spectral gap (physics)
• Spectral radius