The role of detachment of links in scale-free networks

  title={The role of detachment of links in scale-free networks},
  author={Petr L{\'a}nsk{\'y} and Federico Polito and Laura Sacerdote},
Real-world networks may exhibit detachment phenomenon determined by the cancelling of previously existing connections. We discuss a tractable extension of Yule model to account for this feature. Analytical results are derived and discussed both asymptotically and for a finite number of links. Comparison with the original model is performed in the supercritical case. The first-order asymptotic tail behavior of the two models is similar but differences arise in the second-order term. We… 

Figures from this paper

Generalized Nonlinear Yule Models
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the
Uniform Preferential Selection Model for Generating Scale-free Networks
This paper proposes a model that describes the degree distribution for the whole range of k > 0, i.e., before and after k m i n and demonstrates that the degree distributions of the graphs generated by this model match well with those of the real-world graphs.
Analysis of a Model for Generating Weakly Scale-free Networks
This paper proposes a model that describes this particular degree distribution for the whole range of $k>0$ and performs comprehensive mathematical analysis of the model in the discrete domain and compares the degree distribution generated by these models with that of real-world networks.
Generating Graphs by Creating Associative and Random Links Between Existing Nodes
This paper proposes a new generative model for generating realistic networks that is a blend of three key ideas namely preferential attachment, associativity of social links and randomness in real networks and gives both qualitative and quantitative results for clarity.
Random Graphs Associated to Some Discrete and Continuous Time Preferential Attachment Models
We give a common description of Simon, Barabási–Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model,
On a Two-Parameter Yule-Simon Distribution
  • E. Baur, J. Bertoin
  • Mathematics
    A Lifetime of Excursions Through Random Walks and Lévy Processes
  • 2021
We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin [2019] in the context of a preferential attachment algorithm with
Studies on generalized Yule models
  • F. Polito
  • Mathematics
    Modern Stochastics: Theory and Applications
  • 2018
We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the $OS$ property, while for the growth of species we use
On the continuous-time limit of the Barabási-Albert random graph


Degree distributions of evolving networks
In this paper, we propose a simple evolving network model with link and node removals as well as additions and show that this evolving network is scale free with a degree exponent varying in (1,4]
Multifractal properties of growing networks
We introduce a new family of models for growing networks. In these networks new edges are preferentially attached to vertices with a higher number of connections, and new vertices are created by
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.
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.
World Wide Web scaling exponent from Simon's 1955 model.
  • S. Bornholdt, Holger Ebel
  • Physics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
A simple and elegant model for scaling phenomena in general copy- and growth-processes as proposed by Simon in 1955 is recalled and when combined with an experimental measurement of network growth in the World Wide Web, this classical model is able to model the in-link dynamics and predicts the scaling exponent gamma=2.1 in accordance with observation.
Scale-Free Networks: A Decade and Beyond
An avalanche of research has shown that many real networks, independent of their age, function, and scope, converge to similar architectures, a universality that allowed researchers from different disciplines to embrace network theory as a common paradigm.
The fractal properties of Internet
It is suggested that a planning of few big links, acting as information highways, may noticeably increase the efficiency of the net without affecting its robustness, and an appropriate figure of merit is introduced.
Preferential attachment growth model and nonextensive statistical mechanics
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.