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Networks: An Introduction

Mark Newman

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet ... 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


Mathematics of networks: An introduction to the mathematical tools used in the study of networks, tools that will be important to many subsequent developments

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/9780199206650.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the basic theoretical tools used to describe and analyze networks, most of which come from graph theory, the branch of mathematics that deals with networks. Topics covered ... More


Introduction to graphs

Guido Caldarelli

in Scale-Free Networks: Complex Webs in Nature and Technology

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199211517
eISBN:
9780191705984
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211517.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This introductory chapter provides the basics of the graph theory used in the book.


Introduction to combinatorial optimization

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter provides an elementary introduction to some basic concepts in theoretical computer science. It includes basic notions of graph theory and an informal introduction to computational ... More


The bridges of Königsberg: Graph theory

Iwo Białynicki-Birula and Iwona Białynicka-Birula

in Modeling Reality: How Computers Mirror Life

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198531005
eISBN:
9780191713033
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198531005.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A simple idea of drawing crude sketches made of line segments to visualize the solutions of some problems has developed over the years into a sophisticated branch of mathematics: graph theory. Simple ... More


The Structure of Complex Networks: Theory and Applications

Ernesto Estrada

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199591756
eISBN:
9780191774959
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199591756.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book is devoted to the analysis of the structure of complex networks by combining results from algebraic, topological, and extremal graph theory with statistical and molecular physics, as well ... More


Mathematics of 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/9780198805090.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic ... 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


Network Dynamics

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A language of nodes and links, degree and moments, and adjacency matrix and distance matrix, among others, is defined and used to capture the wide range of different types and properties of network ... 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


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