  The bloom of complex network study, in particular, with respect to scale-free
ones, is considerably triggering the research of scale-free graph itself.
Therefore, a great number of interesting results have been reported in the
past, including bounds of diameter. In this paper, we focus mainly on a problem
of how to analytically estimate the lower bound of diameter of scale-free
graph, i.e., how small scale-free graph can be. Unlike some pre-existing
methods for determining the lower bound of diameter, we make use of a
constructive manner in which one candidate model $\mathcal{G^*} (\mathcal{V^*},
\mathcal{E^*})$ with ultra-small diameter can be generated. In addition, with a
rigorous proof, we certainly demonstrate that the diameter of graph
$\mathcal{G^{*}}(\mathcal{V^{*}},\mathcal{E^{*}})$ must be the smallest in
comparison with that of any scale-free graph. This should be regarded as the
tight lower bound.
