algebraic connectivity of a graph

Let $L(G)$ be the Laplacian matrix (http://planetmath.org/LaplacianMatrixOfAGraph) of a finite connected graph $G$ with $n$ vertices. Let the eigenvalues of $L(G)$ be denoted by ${\lambda }_1\le {\lambda }_2\le \mathrm{\cdots }\le {\lambda }_n$, which is the usual notation in spectral graph theory. The connectivity of $G$ is ${\lambda }_2$. The usual notation for the algebraic connectivity is $a(G)$. The parameter is a measure of how well the graph is connected. For example, $a(G)\ne 0$ if and only if $G$ is connected.

Title	algebraic connectivity of a graph
Canonical name	AlgebraicConnectivityOfAGraph
Date of creation	2013-03-22 17:04:37
Last modified on	2013-03-22 17:04:37
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	9
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 05C50
Defines	algebraic connectivity