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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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