Evolution of networks

  title={Evolution of networks},
  author={Sergey N. Dorogovtsev and Jos{\'e} F. F. Mendes},
  journal={Advances in Physics},
  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… 

Theory of Random Networks and Their Role in Communications Networks

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.

Stochastically evolving networks.

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

Temporal evolution of the degree distribution of alters in growing networks

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.

Random Graphs and Complex Networks

  • R. Hofstad
  • Computer Science
    Cambridge Series in Statistical and Probabilistic Mathematics
  • 2016
This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.

The topology and dynamics of complex networks

It is demonstrated that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate the virus.

Synchronization in Complex Dynamical Networks and Its Applications

The economic-cycle synchronous phenomenon in the World Trade Web, a scale-free type of network, is used to illustrate an application of the network synchronization mechanism.

Complex Networks: Structure and Dynamics

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.

Evolving dynamical networks 1

  • Computer Science
  • 2013
This special issue contains a collection of research papers from a broad spectrum of topics related to modeling, analysis, and control of evolving dynamical networks, including stability and bifurcation theory, information and ergodic theory, averaging methods, and mathematical control theory.

Dynamic and Topological Interplay in Adaptive Networks

This chapter is devoted to adaptive networks which combine topological evolution of the network with dynamics in the network nodes – a property which yields a rich dynamical interplay between the state and the topology of thenetwork.



Random networks created by biological evolution.

  • F. SlaninaM. Kotrla
  • Computer Science
    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.

Statistical mechanics of complex networks

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.

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

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.

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

The observed average connectivity in a nervous structure or in a biological genome is hard to explain in a framework of networks with a static architecture, so combinato-rial as well as numerical methods provide a quite detailed picture about their dynamical properties and correspondence with Boolean Networks.

On the properties of small-world network models

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

Evolution of the social network of scienti $ c collaborations

The results indicate that the co-authorship network is scale-free, and that the network evolution is governed by preferential attachment, a8ecting both internal and external links, and a simple model is proposed that captures the network’s time evolution.

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

  • S. JainS. Krishna
  • Biology
    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.

Collective dynamics of ‘small-world’ networks

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.