Let \(A\) be the adjacency matrix of the graph \(G\) and let \(D\) be the diagonal matrix with \(i\)-th diagonal entry equal to the valence of the \(i\)-th vertex of \(G\). The Laplacian matrix of \(G\) is \(D-A\). The all-ones vector lies in the kernel of \(D-A\), so its least eigenvalue is zero. Let \(\lambda_ 2\) denote its second smallest eigenvalue. The mean distance of \(G\) is the mean of the distance between distinct pairs of vertices from \(G\). The paper under review provides upper and lower bounds on the diameter and mean distance of \(G\) in terms of \(\lambda_ 2\). By way of example, if \(G\) has \(n\) vertices and maximum valency \(\Delta\) then the diameter of \(G\) is at most \[ 2\left\lceil{\Delta+\lambda_ 2\over 4\lambda_ 2}\log(n-1)\right\rceil. \] Another, more complicated, upper bound on the diameter of \(G\) is derived, which improves an older bound due to \textit{N. Alon} and \textit{V. D. Milman} \([\lambda_ 1\), isoperimetric inequalities for graphs and superconcentrators, J. Comb. Theory, Ser. B 38, 73-88 (1985; Zbl 0549.05051)].