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Scale-free networks are quite popular nowadays since many systems are wellrepresented by such structures. In order to study these systems, several modelswere proposed. However, most of them do not take into account the node-to-nodeEuclidean distance, i.e., the geographical distance. In real networks, thedistance between sites can be very relevant, e.g., those cases where it isintended to minimize costs. Within this scenario we studied the role ofdimensionality $d$ in the Bianconi-Barab\'asi model with a preferentialattachment growth involving Euclidean distances. The preferential attachment inthis model follows the rule $\Pi_{i} \propto \eta_i k_i/r_{ij}^{\alpha_A}$ $(1\leq i < j; \alpha_A \geq 0)$, where $\eta_i$ characterizes the fitness of the$i$-th site and is randomly chosen within the $(0,1]$ interval. We verifiedthat the degree distribution $P(k)$ for dimensions $d=1,2,3,4$ are well fittedby $P(k) \propto e_q^{-k/\kappa}$, where $e_q^{-k/\kappa}$ is the$q$-exponential function naturally emerging within nonextensive statisticalmechanics. We determine the index $q$ and $\kappa$ as functions of thequantities $\alpha_A$ and $d$, and numerically verify that both present auniversal behavior with respect to the scaled variable $\alpha_A/d$. The samebehavior also has been displayed by the dynamical $\beta$ exponent whichcharacterizes the steadily growing number of links of a given site.

Role of dimensionality in preferential attachment growth in the Bianconi-Barab\'asi model