# Evolution of networks

@article{Dorogovtsev2002EvolutionON, title={Evolution of networks}, author={S. N. Dorogovtsev and J. Mendes}, journal={Advances in Physics}, year={2002}, volume={51}, pages={1079 - 1187} }

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale… Expand

#### 3,032 Citations

Theory of Random Networks and Their Role in Communications Networks

- Computer Science
- Web Dynamics
- 2004

The goal of this review is to show from a physicist’s point of view the many problems addressed by such networks and the present understanding within the field. Expand

Stochastically evolving networks.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

We discuss a class of models for the evolution of networks in which new nodes are recruited into the network at random times, and links between existing nodes that are not yet directly connected may… Expand

Temporal evolution of the degree distribution of alters in growing networks

- Computer Science
- Network Science
- 2018

This paper provides the first theoretical study of the temporal evolution of the nearest-neighbor degree distribution for arbitrary networks (with any size) in arbitrary times and demonstrates that the existing result in the literature on the asymptotic behavior of the Pearson coefficient of growing networks under the preferential attachment mechanism is incorrect. Expand

The topology and dynamics of complex networks

- Engineering
- 2005

We start with a brief introduction about the
topological properties of real networks. Most real networks are
scale-free, being characterized by a power-law degree distribution.
The scale-free nature… Expand

Synchronization in Complex Dynamical Networks and Its Applications

- 2003

In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated increasing interest in further studying the underlying… Expand

Complex networks: Structure and dynamics

- Physics
- 2006

Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly… Expand

Evolving dynamical networks 1

- 2013

Networks of dynamical systems are common models for many problems in physics, engineering, chemistry, biology, and social sciences [1–3]. Recently, considerable attention has been devoted to… Expand

Dynamic and Topological Interplay in Adaptive Networks

- Mathematics
- 2009

Theory and applications of complex networks pervade nonlinear sciences. This chapter is devoted to adaptive networks which combine topological evolution of the network with dynamics in the network… Expand

Complex Networks: Structure and Dynamics

- Computer Science
- 2014

The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering. Expand

Michaelis-Menten Dynamics in Complex Heterogeneous Networks

- Mathematics, Biology
- 2005

This paper reports on the dynamics of a Michaelis–Menten like model when the topological features of the underlying network resemble those of real biological networks, dealing with a complex heterogeneous network characterized by a power-law degree distribution coupled to a continuous dynamics for each network's component. Expand

#### References

SHOWING 1-10 OF 453 REFERENCES

Random networks created by biological evolution.

- Mathematics, Physics
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that the underlying network can evolve by adding and removing sites, and various geometrical properties of the network are studied. Expand

Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamical Rules *

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average… Expand

Scaling properties of scale-free evolving networks: continuous approach.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is shown that permanent random damage to a growing scale-free network-a permanent deletion of some links-radically changes the values of the scaling exponents, and the limits of their validity are indicated. Expand

Evolution of the social network of scienti $ c collaborations

- 2002

The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it o8ers one of the most extensive database to date on social networks. By mapping the… Expand

Statistical mechanics of complex networks

- Computer Science, Physics
- ArXiv
- 2001

A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. Expand

On the properties of small-world network models

- Physics
- 1999

Abstract:We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties… Expand

Evolution of the social network of scientific collaborations

- Sociology, Computer Science
- 2002

The results indicate that the co-authorship network of scientists is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links, and a simple model is proposed that captures the network's time evolution. Expand

Dynamics of directed graphs: the world-wide Web

- Mathematics, Physics
- 2001

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links… Expand

A model for the emergence of cooperation, interdependence, and structure in evolving networks.

- Physics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 2001

A simple mathematical model is described for the evolution of an idealized chemical system to study how a network of cooperative molecular species arises and evolves to become more complex and structured. Expand

Anomalous percolation properties of growing networks.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking is described and exact results for the size and the distribution of vertices among connected components are obtained. Expand