  We derived surface brightness profiles in the \emph{g} band for 170 Small
Magellanic Cloud (SMC) star clusters (SCs) mainly located in the central region
of the galaxy. We provide a set of homogeneous structural parameters obtained
by fitting Elson, Fall \& Freeman (EFF) and King models. Through a careful
analysis of their colour-magnitude diagrams (CMDs) we also supply the ages for
a subsample of 134 SCs. For the first time, such a large sample of SCs in the
SMC is homogeneously characterized in terms of their sizes, luminosities and
masses, widening the probed region of the parameter space, down to hundreds of
solar masses. We used these data to explore the evolution of the SC's
structural parameters with time. In particular, we confirm the existence of a
physical mechanism that induces an increase of the core radius after 0.3-1.0
Gyr. We suggest that cluster mass could be the main parameter driving the inner
expansion, as none of the SCs having $\log (M/M_{\odot}) \leq 3.5$~dex analysed
in this work undergoes to such an expansion. We also detected a mass-size
relationship almost over the entire range of SCs masses investigated here.
Finally, our data suggest that globally the SMC SC system is dynamically
evolved.
