Dynamic scaling, data-collapse and self-similarity in Barabási and Albert networks

  title={Dynamic scaling, data-collapse and self-similarity in Barab{\'a}si and Albert networks},
  author={M. K. Hassan and M. Hassan and N. I. Pavel},
In this paper, we show that if each node of the Barabasi–Albert (BA) network is characterized by the generalized degree q, i.e. the product of their degree k and the square root of their respective birth time, then the distribution function F(q, t) exhibits dynamic scaling F(q, t → ∞) ~ t−1/2(q/t1/2) where (x) is the scaling function. We verified it by showing that a series of distinct F(q, t) versus q curves for different network sizes N collapse onto a single universal curve if we plot t1/2F… Expand
Universality class of explosive percolation in Barabási-Albert networks
This work study explosive percolation in Barabási-Albert network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process finds that the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR. Expand
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Recently, we have shown that if the $i$th node of the Barab\'{a}si-Albert (BA) network is characterized by the generalized degree $q_i(t)=k_i(t)t_i^\beta/m$, where $k_i(t)\sim t^\beta$ and $m$ areExpand
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  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
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Evolution of networks
The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated. Expand
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. Expand
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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. Expand
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  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
It is shown that the probability of a pair of scientists collaborating increases with the number of other collaborators they have in common, and that the probabilities of a particular scientist acquiring new collaborators increases withThe number of his or her past collaborators. Expand
The Structure and Function of Complex Networks
  • M. Newman
  • Physics, Computer Science
  • SIAM Rev.
  • 2003
Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks. Expand
Preferential attachment in the protein network evolution.
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