## 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

## 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

## 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

## 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

## 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

## 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.

## 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

## 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

## 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

## Landscape Connectivity

*Kimberly A. With*

### in Essentials of Landscape Ecology

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198838388
- eISBN:
- 9780191874697
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198838388.003.0005
- Subject:
- Biology, Ecology, Biodiversity / Conservation Biology

Landscape connectivity is essential for maintaining ecological flows across landscapes. Processes as diverse as dispersal; gene flow; the flow of water, materials and nutrients; the spread of ... More

## Graph Theory for Temporal Structure

*Jason Yust*

### in Organized Time: Rhythm, Tonality, and Form

- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780190696481
- eISBN:
- 9780190696511
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190696481.003.0014
- Subject:
- Music, Theory, Analysis, Composition

This chapter introduces mathematical graph theory and develops graph-theory concepts that are useful for temporal networks. By generating chord progressions from networks, the potential musical and ... More

## The Yablo Paradox: An Essay on Circularity

*Roy T Cook*

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199669608
- eISBN:
- 9780191760600
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199669608.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book examines the Yablo paradox—a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence—with special attention paid to the ... More