# Stochastic Weighted Fractal Networks

@article{Carletti2010StochasticWF, title={Stochastic Weighted Fractal Networks}, author={Timot{\'e}o Carletti}, journal={arXiv: Statistical Mechanics}, year={2010} }

In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both classes can be completely analytically characterized in terms of the involved parameters. The proposed algorithms improve and extend the framework of weighted fractal networks recently proposed in (T. Carletti & S. Righi, in press Physica A, 2010)

## 3 Citations

Weighted Fractal Networks

- Mathematics, Physics
- 2010

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved…

Evolving Models for Dynamic Weighted Complex Networks

- Computer SciencePrinciples of Social Networking
- 2021

This chapter will cover the evolution of weighted complex networks and evolving models to generate different types of synthetic weighted networks, including undirected, directed, signed, multilayered, community, and core–periphery structured weighted networks.

A Survey of Evolving Models for Weighted Complex Networks based on their Dynamics and Evolution

- Computer Science, PhysicsArXiv
- 2020

This chapter discusses the evolution of weighted networks and evolving models to generate different types of synthetic weighted networks, including undirected, directed, signed, multilayered, community, and core-periphery structured weighted networks.

## References

SHOWING 1-10 OF 58 REFERENCES

Weighted Fractal Networks

- Mathematics, Physics
- 2010

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved…

FRACTALS IN PHYSICS

- Physics
- 1990

We give a brief overview of the impact of fractal geometry on physical sciences. In particular we will describe the prototype of fractal growth models and the recent developments in the direction of…

Weighted evolving networks: coupling topology and weight dynamics.

- Medicine, PhysicsPhysical review letters
- 2004

A model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution and yields a nontrivial time evolution of vertices' properties and scale-free behavior for the weight, strength, and degree distributions.

Models of Fractal River Basins

- Geology, Physics
- 1998

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant…

Incompatibility networks as models of scale-free small-world graphs

- Computer Science
- 2007

A mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs are made, found to be peculiarly rich.

Deterministic Scale-free Networks Created in a Recursive Manner

- Mathematics, Physics2006 International Conference on Communications, Circuits and Systems
- 2006

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the…

Fractal Growth Phenomena

- Mathematics
- 1989

Foreword, B. Mandelbrot introduction fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces…

Minimal models of weighted scale-free networks

- Mathematics, Physics
- 2004

We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially…

Fractals everywhere

- Mathematics, Computer Science
- 1988

Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal…

Modeling the evolution of weighted networks.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

A general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution, which yields a nontrivial time evolution of vertices' properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules.