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

@article{Nunes2017RoleOD,
  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},
  year={2017},
  volume={2017},
  pages={093402}
}
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… 

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References

SHOWING 1-10 OF 27 REFERENCES
Preferential attachment growth model and nonextensive statistical mechanics
TLDR
The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs Γ-space for Hamiltonian systems) a scale-free network.
Role of dimensionality in complex networks
TLDR
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
TLDR
This work explores the possibility to interpret as a "gas" the dynamical self-organized scale-free network recently introduced by Kim et al. (2005), and numerically shows that this system exhibits nonextensive statistics in the degree distribution, and calculates how the entropic index q depends on α.
Network geometry with flavor: From complexity to quantum geometry.
TLDR
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.
Spatial Networks
Emergence of scaling in random networks
TLDR
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
TLDR
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
TLDR
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.
...
1
2
3
...