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 Spectral gap conjecture
References
External links "Impossible-Seeming Surfaces Confirmed Decades After Conjecture". Quanta Magazine. 2022-06-02.