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# algebraic connectivity of a graph

Let $L(G)$ be the Laplacian matrix
of a finite connected graph $G$ with $n$ vertices. Let the eigenvalues
of $L(G)$ be denoted by
$\lambda_{1}\leq\lambda_{2}\leq\cdots\leq\lambda_{n}$, which
is the usual notation in spectral graph theory.
The *algebraic 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, $a(G)\not=0$ if and only if $G$ is connected.

# References

- 1
Fieldler, M. Algebraic connectivity of graphs,
*Czech. Math. J.*23 (98) (1973) pp. 298-305. - 2
Merris, R. Laplacian matrices of graphs: a survey,
*Lin. Algebra and its Appl.*197/198 (1994) pp. 143-176.

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algebraic connectivity

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## Mathematics Subject Classification

05C50*no label found*

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