Scale-free networks are quite popular nowadays since many systems are well represented by such structures. In order to study these systems, several models were proposed. However, most of them do not take into account the node-to-node Euclidean distance, i.e. the geographical distance. In real networks, the distance between sites can be very relevant, e.g. those cases where it is intended to minimize costs. Within this scenario we studied the role of dimensionality d in the Bianconi–Barabási model with a preferential attachment growth involving Euclidean distances.

The preferential attachment in this model follows the rule  , where  characterizes the fitness of the ith site and is randomly chosen within the  interval. We verified that the degree distribution  for dimensions  are well fitted by , where  is the q-exponential function naturally emerging within nonextensive statistical mechanics. We determine the index q and κ as functions of the quantities  and d, and numerically verify that both present a universal behavior with respect to the scaled variable . The same behavior also has been displayed by the dynamical β exponent which characterizes the steadily growing number of links of a given site.

T.C Nunes, S. Brito, L.R. da Silva, C. Tsallis, Role of dimensionality in preferential attachment growth in the Bianconi-Barabasi model, J. Stat. Mech. (2017) 093402