Algebraic connectivity of a finite simple graph

algConn G is the algebraic connectivity of a finite simple graph G: the second-smallest eigenvalue of its Laplacian matrix L(G) = D(G) - A(G).

Matrix.IsHermitian.eigenvalues₀ lists the eigenvalues of a Hermitian matrix in antitone (descending) order, so the smallest eigenvalue (always 0 for a graph Laplacian) sits at index card V - 1, and the second-smallest — the algebraic connectivity λ₂ — at index card V - 2.

noncomputable def ACMax.algConn {V : Type u_1} [Fintype V] [Nonempty V] (G : SimpleGraph V) : ℝ

Algebraic connectivity of a finite simple graph: the second-smallest eigenvalue of the graph Laplacian L(G) = D(G) - A(G).

Equations

• ACMax.algConn G = ⋯.eigenvalues₀ ⟨Fintype.card V - 2, ⋯⟩