# EVOLVING SCALE-FREE NETWORK MODEL WITH TUNABLE CLUSTERING

@article{Wang2005EVOLVINGSN, title={EVOLVING SCALE-FREE NETWORK MODEL WITH TUNABLE CLUSTERING}, author={Bing Wang and Huanwen Tang and Zhongzhi Zhang and Zhilong Xiu}, journal={International Journal of Modern Physics B}, year={2005}, volume={19}, pages={3951-3959} }

The Barabasi–Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability p, we add a new node with m edges which preferentially link to the nodes presented in the network; with probability 1-p, we add m edges among the present nodes. A node is preferentially selected by its degree to add an edge randomly among its neighbors. Using the continuum theory and the rate equation method we get the analytical expressions of the power…

## 19 Citations

An Evolving Network Model With Local-World Structure ∗

- Physics
- 2009

In this paper, a new local-world evolving network model including triad formation mechanism is proposed and studied. Analytical expressions for degree distribution and cluster- ing coefficient are…

Evolving scale-free network model with tunable clustering and APL

- Computer Science2008 Chinese Control and Decision Conference
- 2008

A scale-free network model with tunable clustering and APL is proposed, which indicates that the degree distribution follows power law and the clustering coefficient and the APL can be tuned with tow parameters.

Evolving Scale-Free Local Networks with Fitness and Tunable Clustering

- Computer Science2009 International Conference on Computational Intelligence and Software Engineering
- 2009

The analytical and numerical expressions of the model consistent with the numerical simulations well are indicated, and the model explains the fitter-gets-richer phenomenon in local-world better, and helps us quantificationally comprehend many competitive systems’ evolution in nature and society.

Generating clustered scale-free networks using Poisson based localization of edges

- Computer Science
- 2018

Effects of accelerating growth on the evolution of weighted complex networks

- Computer Science
- 2009

Evolving weighted networks with edge weight dynamical growth

- Materials ScienceKybernetes
- 2012

A simple one‐parameter evolution model of weighted networks is proposed, in which the topological growth combines with the variation of weights, which can generate scale‐free distributions of the degree, node strength and edge weight, as confirmed in many real networks.

PHASE TRANSITION IN THE ISING MODEL ON LOCAL-WORLD EVOLVING NETWORKS

- Physics
- 2008

We study the critical behavior of the Ising model on the local-world evolving network. Monte Carlo simulations with the standard Metropolis local update algorithms are performed extensively on the…

## References

SHOWING 1-10 OF 32 REFERENCES

Structural transitions in scale-free networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A scaling theory is presented to describe the behavior of the generalized models and the mean-field rate equation for clustering and it is solved for a specific case with the result C(k) approximately 1/k for the clustering of a node of degree k.

Highly clustered scale-free networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The model shows stylized features of real-world networks: power-law distribution of degree, linear preferential attachment of new links, and a negative correlation between the age of a node and its link attachment rate.

Growing scale-free networks with tunable clustering.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The standard scale-free network model is extended to include a "triad formation step" and the clustering coefficient is shown to be tunable simply by changing a control parameter---the average number of triad formation trials per time step.

Growing scale-free networks with small-world behavior.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

A simple dynamical model is introduced that unifies the generic features of real networks: scale-free distribution of degree and the small-world effect and derives analytical expressions for the clustering coefficient in two limiting cases: random [C approximately (ln N)(2)/N] and highly clustered (C=5/6) scale- free networks.

Topology of evolving networks: local events and universality

- Computer SciencePhysical review letters
- 2000

A continuum theory is proposed that predicts the connectivity distribution of the network describing the professional links between movie actors as well as the scaling function and the exponents, in good agreement with numerical results.

Evolution of networks with aging of sites

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

It is found both from simulation and analytically that the network shows scaling behavior only in the region alpha<1, when alpha increases from -infinity to 0, and the exponent gamma of the distribution of connectivities grows from 2 to the value for the network without aging.

Emergence of scaling in random networks

- Computer ScienceScience
- 1999

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

- Computer Science
- 2002

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.

Epidemic threshold in structured scale-free networks.

- Computer SciencePhysical review letters
- 2002

A quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs is introduced and verified, suggesting that high clustering (modularity) and degree correlations protect scale-free networks against the spreading of viruses.