Role of dimensionality in preferential attachment growth in the Bianconi–Barabási model

  title={Role of dimensionality in preferential attachment growth in the Bianconi–Barab{\'a}si model},
  author={Thiago C. Nunes and S. G. A. Brito and Luciano R. da Silva and Constantino Tsallis},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
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–Barabasi… 
13 Citations

Figures from this paper

Networks with Growth and Preferential Attachment: Modeling and Applications
It is found that characteristics as homophily, fitness and geographic distance are significant preferential attachment rules to modeling real networks.
Scaling properties of d-dimensional complex networks.
This paper numerically analyzed the time evolution of the connectivity of sites, the average shortest path, the degree distribution entropy, and the average clustering coefficient for d=1,2,3,4 and typical values of α_{A}.
Connecting complex networks to nonadditive entropies
The Boltzmann–Gibbs exponential factor is generically substituted by its q -generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away.
Erratum to “Surname complex network for Brazil and Portugal” [Physica A 499 (2018) 198–207]
We present a study of social networks based on the analysis of Brazilian and Portuguese family names (surnames). We construct networks whose nodes are names of families and whose edges represent
Surname complex network for Brazil and Portugal
Abstract We present a study of social networks based on the analysis of Brazilian and Portuguese family names (surnames). We construct networks whose nodes are names of families and whose edges
Validity and failure of the Boltzmann weight
The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics.
d-Dimensional Classical Heisenberg Model with Arbitrarily-Ranged Interactions: Lyapunov Exponents and Distributions of Momenta and Energies
Through the Lyapunov exponents, an intriguing, and possibly size-dependent, persistence of the non-Boltzmannian behavior even in the α/d>1 regime is observed.
Analytic approaches of the anomalous diffusion: A review
Abstract This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to
Quasi-stationary-state duration in the classical d-dimensional long-range inertial XY ferromagnet.
It is shown that the exponent A(α/d) and the coefficient B(N) present universal behavior (within error bars), comparing the XY and Heisenberg cases, and a scaling for t-QSS is proposed, namely, t_{QSS}∝N^{A( α/d)}e-B(N)(α/ d)^{2}, analogous to a recent analysis carried out for the classical α-Heisenberg inertial model.
Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere
The present review focuses on nonadditive entropies generalizing Boltzmann–Gibbs statistical mechanics and their predictions, verifications, and applications in physics and elsewhere.


Preferential attachment growth model and nonextensive statistical mechanics
We introduce a two-dimensional growth model where every new site is located, at a distance r from the barycenter of the pre-existing graph, according to the probability law 1/r2 + αG (αG > 0), and is
Role of dimensionality in complex networks
D-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through q-statistics are introduced and it is numerically verified that the q-exponential degree distributions exhibit universal dependences on the ratio αA/d.
Nonextensive aspects of self-organized scale-free gas-like networks
We explore the possibility to interpret as a "gas" the dynamical self-organized scale-free network recently introduced by Kim et al. (2005). The role of "momentum" of individual nodes is played by
Network geometry with flavor: From complexity to quantum geometry.
This work introduces the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics, and shows that NGF admits a quantum mechanical description in terms of associated quantum network states.
Growing random networks with fitness
Three models of growing random networks with fitness-dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is
Spatial Networks
This work will expose thoroughly the current state of the understanding of how the spatial constraints affect the structure and properties of these networks, and review the most recent empirical observations and the most important models of spatial networks.
Emergence of scaling in random networks
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Collective dynamics of ‘small-world’ networks
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Preferential Attachment Scale-Free Growth Model with Random Fitness and Connection with Tsallis Statistics(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its
Competition and multiscaling in evolving networks
This work finds that competition for links translates into multiscaling, i.e. a fitness dependent dynamic exponent, allowing fitter nodes to overcome the more connected but less fit ones.