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## NON-EQUILIBRIUM NETWORKS

*S. N. Dorogovtsev and J. F. F. Mendes*

### in Evolution of Networks: From Biological Nets to the Internet and WWW

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0006
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter describes in detail the preferential attachment mechanism. It starts with growing networks with exponential degree distributions, and then considers structural characteristics of basic ... More

## The large-scale structure of networks: A discussion of some of the recurring patterns and structures revealed when we apply the concepts developed in previous chapters to the study of real-world networks

*M. E. J. Newman*

### in Networks: An Introduction

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The previous chapters looked at different types of natural and man-made networks and techniques for determining their structure, the mathematics used to represent networks formally, and the measures ... More

## POPULARITY IS ATTRACTIVE

*S. N. Dorogovtsev and J. F. F. Mendes*

### in Evolution of Networks: From Biological Nets to the Internet and WWW

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter explains the preferential attachment mechanism in application to growing networks. Illustrating models show that proportional preferential attachment in recursive networks leads to ... More

## WHAT ARE NETWORKS?

*S. N. Dorogovtsev and J. F. F. Mendes*

### in Evolution of Networks: From Biological Nets to the Internet and WWW

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198515906
- eISBN:
- 9780191705670
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515906.003.0002
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter introduces the basic characteristics and notions of graph theory and the science of networks: degree, degree distribution, clustering coefficient, the average length of the shortest path ... More

## Classical random graphs

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter gives insight into the simplest and most studied random networks: the classical random graphs. The Erdös–Rényi and Gilbert models are described, and some of their properties and ... More

## First steps towards networks

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the basic notions of graph theory and discusses the starting point of network science, namely the Konigsberg bridge problem. A few examples of different graphs, lattices, and ... More

## The configuration model

*Mark Newman*

### in Networks

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A discussion of the most fundamental of network models, the configuration model, which is a random graph model of a network with a specified degree sequence. Following a definition of the model a ... More

## Fundamental network algorithms: A discussion of some of the most important and fundamental algorithms for performing network calculations on a computer

*M. E. J. Newman*

### in Networks: An Introduction

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199206650
- eISBN:
- 9780191594175
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206650.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter looks at the algorithms used to perform network calculations. It starts with some simple algorithms for calculating quantities such as degrees, degree distributions, and clustering ... More

## The structure of real-world networks

*Mark Newman*

### in Networks

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter brings together the ideas and techniques developed in previous chapters, applying them to a range of real-world networks to describe and understand the structure of those networks. ... More

## Adjacency relations in networks

*Ernesto Estrada*

### in The Structure of Complex Networks: Theory and Applications

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199591756
- eISBN:
- 9780191774959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199591756.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter explains the concepts of adjacency between nodes in a network; the adjacency operator of a network and its matrix representation; and the meaning of degree, degree distributions, and ... More

## Random graphs

*Mark Newman*

### in Networks

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties ... More

## Definitions and concepts

*A.C.C. Coolen, A. Annibale, and E.S. Roberts*

### in Generating Random Networks and Graphs

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198709893
- eISBN:
- 9780191780172
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198709893.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A network is specified by its links and nodes. However, it can be described by a much wider range of interesting and important topological features. This chapter introduces how a network can be ... More

## Basic Structural Properties

*Ginestra Bianconi*

### in Multilayer Networks: Structure and Function

- Published in print:
- 2018
- Published Online:
- July 2018
- ISBN:
- 9780198753919
- eISBN:
- 9780191815676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198753919.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter the basic structural properties of multilayer networks are given. This chapter reveals that on multilayer networks the most basic structural properties of a network such as the degree ... More

## Integrative ecological genomics

*Nico M. van Straalen and Dick Roelofs*

### in An Introduction to Ecological Genomics

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199594689
- eISBN:
- 9780191774812
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199594689.003.0304
- Subject:
- Biology, Ecology

Systems biology is a new discipline of the life sciences that aims to integrate the knowledge generated by genomics, transcriptomics, proteomics, and metabolomics to obtain a picture of the ... More

## Introduction

*Ernesto Estrada*

### in The Structure of Complex Networks: Theory and Applications

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199591756
- eISBN:
- 9780191774959
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199591756.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter explains the basic concepts of networks, the history of the field, and the necessity of studying their structure. It provides a global classification of networks with ... More

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