## INTRODUCTION

*Mathew Penrose*

### in Random Geometric Graphs

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0001
- Subject:
- Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More

## FURTHER ADVANCED TECHNIQUES

*Rolf Niedermeier*

### in Invitation to Fixed-Parameter Algorithms

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566076
- eISBN:
- 9780191713910
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566076.003.0011
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter surveys further important techniques for designing fixed-parameter algorithms. These include color-coding, integer linear programming, iterative compression, greedy localization, and ... More

## Very Fast Oscillations

*Roger D. Roger and Miles A. Whittington*

### in Cortical Oscillations in Health and Disease

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780195342796
- eISBN:
- 9780199776276
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195342796.003.0010
- Subject:
- Neuroscience, Molecular and Cellular Systems, Development

VFO occurs in in vitro models when chemical receptors are blocked. In particular, VFO does not require GABAA receptors, even though interneurons fire at high rates during in vivo very fast ... More

## Social Interactions: Theory and Empirics

*Yannis M. Ioannides*

### in From Neighborhoods to Nations: The Economics of Social Interactions

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691126852
- eISBN:
- 9781400845385
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691126852.003.0002
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter discusses the theory and empirics of social interactions, with particular emphasis on the role of social context in individual decisions. It begins by introducing a sequence of models ... More

## FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

*Andrew Goodall*

### in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.003.0007
- Subject:
- Mathematics, Probability / Statistics

This article reviews basic techniques of Fourier analysis on a finite abelian group Q, with subsequent applications in graph theory. These include evaluations of the Tutte polynomial of a graph G in ... More

## The Regress Objection

*Alexander Bird*

### in Nature's Metaphysics: Laws and Properties

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199227013
- eISBN:
- 9780191711121
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227013.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology

It is often claimed (e.g., by Swinburne, Armstrong, and Lowe) that the view that all natural properties are potencies leads to a vicious regress or circularity. The possible interpretations of this ... More

## 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

## Algorithmic aspects

*J. L. Ramírez Alfonsín*

### in The Diophantine Frobenius Problem

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568209
- eISBN:
- 9780191718229
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568209.003.0001
- Subject:
- Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

This chapter is devoted to the computational aspects of the Frobenius number. After discussing a number of methods to solve FP when n = 3 (some of these procedures make use of diverse concepts, such ... More

## Empirical Identification of the Vector Autoregression: The Causes and Effects of US M2 *

*Kevin D. Hoover, Selva Demiralp, and Stephen J. Perez*

### in The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199237197
- eISBN:
- 9780191717314
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199237197.003.0002
- Subject:
- Economics and Finance, Econometrics

The M2 monetary aggregate is monitored by the Federal Reserve, using a broad brush theoretical analysis and an informal empirical analysis. This chapter illustrates empirical identification of an ... More

## Graph Theory: A Look Back—The Road Ahead

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0013
- Subject:
- Mathematics, Applied Mathematics

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution ... 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

## Urban Magic: Concluding Remarks

*Yannis M. Ioannides*

### in From Neighborhoods to Nations: The Economics of Social Interactions

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691126852
- eISBN:
- 9781400845385
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691126852.003.0010
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter considers the prospect of a deeper understanding of social interactions in urban settings as well as their significance for the functioning and future role of cities and regions. It ... 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

## 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

## The Fascinating World of Graph Theory

*Ping Zhang, Gary Chartrand, and Arthur Benjamin*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.001.0001
- Subject:
- Mathematics, Applied Mathematics

Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, ... More

## The growth of syntax

*Anat Ninio*

### in Language and the Learning Curve: A new theory of syntactic development

- Published in print:
- 2006
- Published Online:
- April 2010
- ISBN:
- 9780199299829
- eISBN:
- 9780191584985
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199299829.003.0006
- Subject:
- Psychology, Cognitive Models and Architectures

This chapter examines the role of the environment in syntactic development, and argues for novel conceptualization derived from complexity theory. According to this view, language is a complex ... More

## Modern graph theory

*LOWELL BEINEKE and ROBIN WILSON*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0015
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

During the first half of the 20th century many classic theorems about graphs were discovered, but it was not until the second half of the century that graph theory emerged as an important field in ... More