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Handbook of Large-Scale Random Networks

Béla Bollobás, Robert Kozma, and Dezső Miklós, editors
Publication Date: 
Number of Pages: 
Bolyai Society Mathematical Studies 18
[Reviewed by
Miklós Bóna
, on

The title is a little bit misleading. The word “handbook” usually denotes a book that surveys a field starting from a relatively low level. Someone with a first-year graduate student’s knowledge of combinatorics can read quite a significant part of the Handbook of Combinatorics, for instance. The book under review, however, is not a general survey. It is a collection of papers on advances in the field of large-scale networks since 2003, when the Handbook of Graphs and Networks was published. The material presented here is based on a workshop organized in Budapest in 2006.

The book has three parts, each consisting of four chapters. The first part is about the mathematical foundations of the subject, the second part is on applications to the biological sciences, and the third part is on other applications, to fields like physics, computer network, and social sciences. See the detailed table of contents for specifics.

Each chapter reads as a survey paper written for the experts, or at the very least, graduate students who have taken a special topic course in the area covered in that chapter. Each chapter has at least two, but usually more authors. An ideal reader of the book may be a mathematician who already knows a lot about large-scale networks, but wants to read about applications in a wide variety of fields, or simply wants to catch up with advances made in the last six years.

Miklós Bóna is Professor of Mathematics at the University of Florida.

Part I: Theoretical Foundations

Chapter 1 Random graphs and branching processes
Bela Bollobas and Oliver Riordan (Cambridge University, UK)

Chapter 2 Sentry Selection in wireless networks
Paul Balister and Bela Bollobas (U of Memphis, TN, and Cambridge University, UK) Amites Sarkar and Mark Walters

Chapter 3 Scaling properties of complex networks and spanning trees
Reuven Cohen and Shlomo Havlin, (MIT, USA)

Chapter 4 Random Tree Growth with Branching Processes – a Survey
Anna Rudas and Balint Toth (Technical University, Budapest, Hungary)

Part II. Large-scale networks in biological systems

Chapter 5 Reaction-diffusion processes in scale-free networks
Michele Catanzaro, Marian Boguna, and Romualdo Pastor-Satorras, (U Catalunya, Barcelona, Spain)

Chapter 6 Toward Understanding the Structure and Function of Cellular Interaction Networks
C. Christensen, J. Thakar and R. Albert (Penn State University, PA, USA)

Chapter 7 Scale-Free Cortical Planar Networks
Bela Bollobas (Cambridge University, UK), Walter J Freeman (UC Berkeley, CA), Robert Kozma (U of Memphis, TN, USA)

Chapter 8 Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity
Nepusz P., Bazso F, (KFKI, Hungarian Academy of Sciences), Negyessy L. (Semmelweis Medical University, Budapest, Hungary) Tusnady G. (Renyi Institute of Mathematics, Hungarian Academy of Sciences)

Part III. Large-scale networks in physics, technology, and the society

Chapter 9 k-clique percolation and clustering
Gergely Palla1, Daniel Abel, Illes J. Farkas, Peter Pollner, Imre Derenyi
Tamas Vicsek (Eotvos University, Budapest, Hungary)

Chapter 10 The inverse problem of evolving networks — with application to social nets
Gabor Csardi, Katherine J. Strandburg, Jan Tobochnik, and Peter Erdi, (KFKI, Hungarian Academy of Sciences, Budapest, Hungary and Kalamazoo College, Mi, USA)

Chapter 11 Learning and Representation: From Compressive Sampling to Szemerédi’s Regularity Lemma
Andras Lorincz (Eotvos University, Budapest, Hungary)

Chapter 12 Telephone Call Network Data Mining: A Survey with Experiments Andras A. Benczur, Karoly Csalogany, Miklos Kurucz, Andras Lukacs, Laszlo Lukacs, David Siklosi (Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary)