Role of dimensionality in preferential attachment growth in the Bianconi-Barabási model
Abstract
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 \Pii \propto ηi k_i/rijα_A (1 ≤slant i < j; αA ≥slant 0) , where ηi 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 q-exponential function naturally emerging within nonextensive statistical mechanics. We determine the index q and κ as functions of the quantities αA 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:
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Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- September 2017
- DOI:
- 10.1088/1742-5468/aa8198
- arXiv:
- arXiv:1705.00014
- Bibcode:
- 2017JSMTE..09.3402N
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 12 pages including 9 figures. To appear in the Journal of Statistical Mechanics (2017)