Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Role of dimensionality in preferential attachment growth in the
  Bianconi-Barab\'asi model   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-Barab\'asi model with a preferential
attachment growth involving Euclidean distances. The preferential attachment in
this 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 verified
that the degree distribution $P(k)$ for dimensions $d=1,2,3,4$ are well fitted
by $P(k) \propto e_q^{-k/\kappa}$, where $e_q^{-k/\kappa}$ is the
$q$-exponential function naturally emerging within nonextensive statistical
mechanics. We determine the index $q$ and $\kappa$ as functions of the
quantities $\alpha_A$ and $d$, and numerically verify that both present a
universal behavior with respect to the scaled variable $\alpha_A/d$. The same
behavior also has been displayed by the dynamical $\beta$ exponent which
characterizes the steadily growing number of links of a given site.

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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn