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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


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


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


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


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


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


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


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.


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


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 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 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 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


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