The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other words, it is the second smallest root of the graph's Laplacian polynomial. This eigenvalue is greater than 0 iff G is a connected graph. The ratio of the Laplacian spectral radius to algebraic connectivity is known as the Laplacian spectral ratio.

connected graph | Fiedler vector | graph eigenvalue | graph spectrum | Laplacian matrix | Laplacian polynomial | Laplacian spectral radius | Laplacian spectral ratio