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The Structure and Dynamics of Networks

Princeton University Press
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The study of networks dates at least as far back as the 1700s and Leonard Euler's famous paper on the Königsberg Bridge Problem. However, network theory is no longer merely of mathematical interest and in fact has become an increasingly popular topic in many fields of study, from sociology to epidemiology to genomics. The Structure and Dynamics of Networks performs an important service by bringing together in one volume a number of papers on network theory, and placing them in historical context. The collection is remarkable for its inclusivity, from a translation of the 1929 short story "Chain-Links" by Frigyes Karinthy through a 2003 article about protein interaction networks by Vazquez et al.

The editors are a varied bunch. Mark Newman is an Associate Professor of Physics and Complex Systems at the University of Michigan and is an External Faculty Member of the Santa Fe Institute. Albert-László Barabási is the Emil T. Hofman Professor of Physics at Notre Dame University and a Concurrent Professor in Computer Science and Engineering. Duncan J. Watts is an Associate Professor of Sociology at Columbia University.

The Structure and Dynamics of Networks is divided into six sections. The introduction, written by the editors, includes a brief history of the study of networks, modern network theory, and an overview of the volume. This is followed by four collections of articles, each of which is preceded by a introductory essay by the volume editors which summarizes each paper and places it in context: Historical Studies, Empirical Studies, Models of Networks, and Applications. The volume closes with a brief essay on what the volume editors see as the future directions of research into networks.

No student or researcher is likely to read all 43 articles contained in The Structure and Dynamics of Networks: instead the volume will serve as an introduction to the topic for the novice and as a resource for the more experienced researcher. In particular, the level of mathematical knowledge required to comprehend the articles ranges from non-existent to highly sophisticated. However, the very clear introductory sections to each chapter provide useful introductions to the various topics, so that a student who is unprepared to understand some of the actual articles can still learn something about the concepts contained in them.

Sarah Boslaugh ( ) is a Senior Statistical Data Analyst in the Department of Pediatrics at the Washington University School of Medicine in St. Louis, MO. She wrote An Intermediate Guide to SPSS Programming: Using Syntax for Data Management with Sage Publications in 2005 and is currently writing Secondary Data Sources for Public Health: A Practical Guide for Cambridge University Press. She is also Editor-in-Chief of The Encyclopedia of Epidemiology which will be published by Sage in 2007.

Date Received: 
Tuesday, May 30, 2006
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Mark Newman, Albert-László Barabási
Publication Date: 
Sarah Boslaugh

Preface ix

Chapter 1. Introduction 1

1.1 A brief history of the study of networks 1
1.2 The "new" science of networks 4
1.3 Overview of the volume 8

Chapter 2: Historical developments 9

Chain-links, F. Karinthy 21
Connectivity of random nets, R. Solomonoff and A. Rapoport 27
On the evolution of random graphs, P. Erdo os and A. Rényi 38
Contacts and influence, I. de S. Pool and M. Kochen 83
An experimental study of the small world problem, J. Travers and S. Milgram 130
Networks of scientific papers, D. J. de S. Price 149
Famous trails to Paul Erd½ os, R. de Castro and J. W. Grossman 155

Chapter 3: Empirical Studies 167

Diameter of the world-wide web, R. Albert, H. Jeong, and A.-L. Barabási 182
Graph structure in the web, A. Broder et al. 183
On power-law relationships of the internet topology, M. Faloutsos, P. Faloutsos, and C. Faloutsos 195
Classes of small-world networks, L.A.N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley 207
The large-scale organization of metabolic networks, H. Jeong et al. 211
The small world of metabolism, A. Wagner and D. Fell 215
Network motifs: Simple building blocks of complex networks, R. Milo et al. 217
The structure of scientific collaboration networks, M. E. J. Newman 221
The web of human sexual contacts, F. Liljeros et al. 227

Chapter 4: Models of networks 229

4.1 Random graph models 229
A critical point for random graphs with a given degree sequence, M. Molloy and B. Reed 240
A random graph model for massive graphs, W. Aiello, F. Chung, and L. Lu 259
Random graphs with arbitrary degree distributions and their applica-tions, M.E.J. Newman, S. H. Strogatz, and D. J. Watts 269
4.2 The small-world model 286
Collective dynamics of 'small-world' networks, D. J. Watts and S. H. Strogatz 301
Small-world networks: Evidence for a crossover picture, M. Barthélémy and L.A.N. Amaral 304
Comment on'Small-world networks: Evidence for crossover picture', A. Barrat, 1999 308
Scaling and percolation in the small-world network model, M.E.J. New-man and D. J. Watts 310
On the properties of small-world networks, A. Barrat and M. Weigt, 2000 321
4.3 Models of scale-free networks 335
Emergence of scaling in random networks, A.-L. Barabási and R. Albert 349
Structure of growing networks with preferential linking, S. N. Dorogov-tsev, J. F. F. Mendes, and A. N. Samukhin 353
Connectivity of growing random networks, P. L. Krapivsky, S. Redner, and F. Leyvraz 357
Competition and multiscaling in evolving networks, G. Bianconi and A.-L. Barabási 361
Universal behavior of load distribution in scale-free networks, K.-I. Goh, B. Kahng, and D. Kim 368
Spectra of "real-world" graphs: Beyond the semicircle law, I. J. Farkas, I. Derényi, A.-L. Barabási, and T. Vicsek 372
The degree sequence of a scale-free random graph process, B. Bol-lobás, O. Riordan, J. Spencer, and G. Tusnády 384
A model of large-scale proteome evolution, R.V. Solé, R. Pastor-Satorras, E. Smith, and T. B. Kepler 396
Modeling of protein interaction networks, A. Vázquez, A. Flammini, A. Maritan, and A. Vespignani 408

Chapter 5: Applications 415

5.1 Epidemics and rumors 415
5.2 Robustness of networks 424
5.3 Searching networks 428
Epidemics with two levels of mixing, F. Ball, D. Mollison, and G. Scalia-Tomba 436
The effects of local spatial structure on epidemiological invasions, M. J. Keeling 480
Small world effect in an epidemiological model, M. Kuperman and G. Abramson 489
Epidemic spreading in scale-free networks, R. Pastor-Satorras and A. Vespignani 493
A simple model of global cascades on random networks, D. J. Watts 497
Error and attack tolerance of complex networks, R. Albert, H. Jeong, and A.-L. Barabási 503
Resilience of the Internet to random breakdowns, R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin 507
Network robustness and fragility: Percolation on random graphs, D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts 510
Authoritative sources in a hyperlinked environment, J. M. Kleinberg 514
Search in power-law networks, L. A. Adamic, R. M. Lukose, A. R. Puniyani, and B. A. Huberman 543
Navigation in a small world, J. M. Kleinberg 551

Chapter 6: Outlook 553

References 559
Index 575

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Monday, July 24, 2006