Role of dimensionality in preferential attachment growth in the BianconiBarabási model
Abstract
Scalefree 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 nodetonode 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 BianconiBarabási model with a preferential attachment growth involving Euclidean distances. The preferential attachment in this model follows the rule \Pi_{i} \propto η_{i} k_i/r_{ij}^{α_A} (1 ≤slant i < j; α_{A} ≥slant 0) , where η_{i} characterizes the fitness of the ith site and is randomly chosen within the (0, 1] interval. We verified that the degree distribution P(k) for dimensions d=1, 2, 3, 4 are well fitted by P(k) \propto e_q^{k/κ} , where e_q^{k/κ} is the qexponential function naturally emerging within nonextensive statistical mechanics. We determine the index q and κ as functions of the quantities α_{A} and d, and numerically verify that both present a universal behavior with respect to the scaled variable α_A/d . The same behavior also has been displayed by the dynamical β exponent which characterizes the steadily growing number of links of a given site.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 September 2017
 DOI:
 10.1088/17425468/aa8198
 arXiv:
 arXiv:1705.00014
 Bibcode:
 2017JSMTE..09.3402N
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages including 9 figures. To appear in the Journal of Statistical Mechanics (2017)