  Deep connections are known to exist between scale-free networks and
non-Gibbsian statistics. For example, typical degree distributions at the
thermodynamical limit are of the form $P(k) \propto e_q^{-k/\kappa}$, where the
$q$-exponential form $e_q^z \equiv [1+(1-q)z]^{\frac{1}{1-q}}$ optimizes the
nonadditive entropy $S_q$ (which, for $q\to 1$, recovers the Boltzmann-Gibbs
entropy). We introduce and study here $d$-dimensional geographically-located
networks which grow with preferential attachment involving Euclidean distances
through $r_{ij}^{-\alpha_A} \; (\alpha_A \ge 0)$. Revealing the connection with
$q$-statistics, we numerically verify (for $d$ =1, 2, 3 and 4) that the
$q$-exponential degree distributions exhibit, for both $q$ and $\kappa$,
universal dependences on the ratio $\alpha_A/d$. Moreover, the $q=1$ limit is
rapidly achieved by increasing $\alpha_A/d$ to infinity.
