BN.com Gift Guide

Small Worlds: The Dynamics of Networks between Order and Randomness

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $18.24
Usually ships in 1-2 business days
(Save 54%)
Other sellers (Paperback)
  • All (15) from $18.24   
  • New (10) from $18.24   
  • Used (5) from $21.02   

Overview

"Duncan Watts has created that rarity of rarities: a book with enough fascinating facts and stories to keep the casual reader turning the pages coupled with enough engaging detail to satisfy the most technically sophisticated reader. Thus, whether you are just curious about the world around you or eager to begin your own small-world research, this is the definitive guide to the fascinating and profound world of small-world networks."—William L. Ditto, Applied Chaos Laboratory, Georgia Institute of Technology

"A good book on a fascinating topic—why two widely separated people are often connected by a small number of steps from friend to friend. We do indeed live in a 'small world.' When something happens so often there must be a reason—Duncan Watts is looking for it."—Gilbert Strang, Department of Mathematics, Massachusetts Institute of Technology

"Duncan Watts's and Steve Strogatz's 1998 Nature paper on 'The collective dynamics of small-world networks' reinvigorated interest in the small-world phenomenon. Now, in Small Worlds, Watts follows up on this work with a detailed but accessible account of small-world networks that will appeal to both scientists and nonscientists. With examples ranging from the Kevin Bacon Game to models for the spread of diseases, Watts provides a clear description of how the structure of small-world networks can be characterized and a sense of how the interconnectivity of such networks can lead to intriguing dynamics. Be sure to tell your friends and their friends about this book."—J. J. Collins, Center for BioDynamics and Department of Biomedical Engineering, Boston University

"Enchanting! A voyage of exploration with fascinating byroads that yet brings the reader to powerful and useable conclusions. This work is worthy of Stanley Milgram exactly because Watts goes well beyond the original visualization while retaining its transparency."—Harrison White, Department of Sociology, Columbia University

"If you are a postgraduate looking to make your name or a seasoned researcher looking for new challenges, this book offers something rare: a chance to get in at the ground floor of a whole new area of research whose variety of exciting applications is exceeded only by their abundance."—Robert A. J. Matthews, Aston University, U.K.

"Small Worlds is outstanding. Watts begins with a simple observation: clustered networks, networks characterized by a large fraction of short ties and a small fraction of 'shortcuts' linking clusters with one another, appear in diverse settings and more frequently than might be expected. Watts then demonstrates that the dynamical behavior of these networks is highly sensitive to structure. The book is must reading, although not easy reading, for social scientists interested in networks, decision-making, and organizational design.(In other words, this is a high-investment, high-payoff book.)"—Marshall W. Meyer, The Wharton School, University of Pennsylvania

"This is a remarkably novel analysis, with implications for a broad range of scientific disciplines, including neurobiology, sociology, ecology, economics, and epidemiology. . . . The results are potentially profoundly important."—Simon A. Levin, Department of Ecology and Evolutionary Biology, Princeton University

"Theoretical research on social networks has been hampered by a lack of models which capture the essential properties of large numbers of graphs with only a few key parameters. All the dyads, triads and acyclic mappings which fill the social network literature lead merely to a long enumeration of special cases. The random graph models introduced by Watts provide a rich foundation for future analytical and empirical research. The applications to dynamics in part 2 illustrate the richness of these models and promise even more exciting work to come."—Larry Blume, Cornell University

Read More Show Less

Editorial Reviews

Quarterly Review of Biology - Peter Kareiva
Playfully and clearly written. . . . [Watts] uses examples adroitly, and mixes abstract theory with real-world anecdotes with superb skill. . . . I have not enjoyed reading a book this much in a long time.
New Scientist - Robert Matthews
[Small Worlds] will be seized on by those seeking a first rough map of this fascinating new mathematical land. Those entering can expect to find some amazing connections between areas of research with apparently nothing in common, such as neurology to business studies. But then, it's a small world.
From the Publisher
"An engaging and informative introduction."—Science

"Playfully and clearly written. . . . [Watts] uses examples adroitly, and mixes abstract theory with real-world anecdotes with superb skill. . . . I have not enjoyed reading a book this much in a long time."—Peter Kareiva, Quarterly Review of Biology

"[Small Worlds] will be seized on by those seeking a first rough map of this fascinating new mathematical land. Those entering can expect to find some amazing connections between areas of research with apparently nothing in common, such as neurology to business studies. But then, it's a small world."—Robert Matthews, New Scientist

"Informally written and aimed at a wide audience, this book shows how mathematics yields new vistas on ubiquitous and seemingly familiar aspects of our world."—Choice

Science
An engaging and informative introduction.
Quarterly Review of Biology
Playfully and clearly written. . . . [Watts] uses examples adroitly, and mixes abstract theory with real-world anecdotes with superb skill. . . . I have not enjoyed reading a book this much in a long time.
— Peter Kareiva
New Scientist
[Small Worlds] will be seized on by those seeking a first rough map of this fascinating new mathematical land. Those entering can expect to find some amazing connections between areas of research with apparently nothing in common, such as neurology to business studies. But then, it's a small world.
— Robert Matthews
Choice
Informally written and aimed at a wide audience, this book shows how mathematics yields new vistas on ubiquitous and seemingly familiar aspects of our world.
Read More Show Less

Product Details

  • ISBN-13: 9780691117041
  • Publisher: Princeton University Press
  • Publication date: 11/24/2003
  • Series: Princeton Studies in Complexity Series
  • Pages: 264
  • Sales rank: 1,234,159
  • Product dimensions: 5.88 (w) x 9.42 (h) x 0.41 (d)

Table of Contents

PREFACE xiii
1 Kevin Bacon, the Small World, and Why It All Matters 3
PART I STRUCTURE 9
2 An Overview of the Small-World Phenomenon 11
2.1 Social Networks and the Small World 11
2.1.1 A Brief History of the Small World 12
2.1.2 Difficulties with the Real World 20
2.1.3 Reframing the Question to Consider All Worlds 24
2.2 Background on the Theory of Graphs 25
2.2.1 Basic Definitions 25
2.2.2 Length and Length Scaling 27
2.2.3 Neighbourhoods and Distribution Sequences 31
2.2.4 Clustering 32
2.2.5 "Lattice Graphs" and Random Graphs 33
2.2.6 Dimension and Embedding of Graphs 39
3 Big Worlds and Small Worlds: Models of Graphs 41
3.1 Relational Graphs 42
3.1.1 a-Graphs 42
3.1.2 A Stripped-Down Model: B-Graphs 66
3.1.3 Shortcuts and Contractions: Model Invariance 70
3.1.4 Lies, Damned Lies, and (More) Statistics 87
3.2 Spatial Graphs 91
3.2.1 Uniform Spatial Graphs 93
3.2.2 Gaussian Spatial Graphs 98
3.3 Main Points in Review 100
4 Explanations and Ruminations 101
4.1 Going to Extremes 101
4.1.1 The Connected-Caveman World 102
4.1.2 Moore Graphs as Approximate Random Graphs 109
4.2 Transitions in Relational Graphs 114
4.2.1 Local and Global Length Scales 114
4.2.2 Length and Length Scaling 116
4.2.3 Clustering Coefficient 117
4.2.4 Contractions 118
4.2.5 Results and Comparisons with B-Model 120
4.3 Transitions in Spatial Graphs 127
4.3.1 Spatial Length versus Graph Length 127
4.3.2 Length and Length Scaling 128
4.3.3 Clustering 130
4.3.4 Results and Comparisons 132
4.4 Variations on Spatial and Relational Graphs 133
4.5 Main Points in Review 136
5 "It's a Small World after All": Three Real Graphs 138
5.1 Making Bacon 140
5.1.1 Examining the Graph 141
5.1.2 Comparisons 143
5.2 The Power of Networks 147
5.2.1 Examining the System 147
5.2.2 Comparisons 150
5.3 A Worm's Eye View 153
5.3.1 Examining the System 154
5.3.2 Comparisons 156
5.4 Other Systems 159
5.5 Main Points in Review 161
PART II DYNAMICS 163
6 The Spread of Infectious Disease in Structured Populations 165
6.1 A Brief Review of Disease Spreading 166
6.2 Analysis and Results 168
6.2.1 Introduction of the Problem 168
6.2.2 Permanent-Removal Dynamics 169
6.2.3 Temporary-Removal Dynamics 176
6.3 Main Points in Review 180
7 Global Computation in Cellular Automata 181
7.1 Background 181
7.1.1 Global Computation 184
7.2 Cellular Automata on Graphs 187
7.2.1 Density Classification 187
7.2.2 Synchronisation 195
7.3 Main Points in Review 198
8 Cooperation in a Small World: Games on Graphs 199
8.1 Background 199
8.1.1 The Prisoner's Dilemma 200
8.1.2 Spatial Prisoner's Dilemma 204
8.1.3 N-Player Prisoner's Dilemma 206
8.1.4 Evolution of Strategies 207
8.2 Emergence of Cooperation in a Homogeneous Population 208
8.2.1 Generalised Tit-for-Tat 209
8.2.2 Win-Stay, Lose-Shift 214
8.3 Evolution of Cooperation in a Heterogeneous Population 219
8.4 Main Points in Review 221
9 Global Synchrony in Populations of Coupled Phase Oscillators 223
9.1 Background 223
9.2 Kuramoto Oscillators on Graphs 228
9.3 Main Points in Review 238
10 Conclusions 240
NOTES 243
BIBLIOGRAPHY 249
INDEX 257

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)