This handbook describes advances in large scale network studies that have taken place in the past 5 years since the publication of the Handbook of Graphs and Networks in 2003. It covers all aspects of large-scale networks, including mathematical foundations and rigorous results of random graph theory, modeling and computational aspects of large-scale networks, as well as areas in physics, biology, neuroscience, sociology and technical areas. Applications range from microscopic to mesoscopic and macroscopic models.

The book is based on the material of the NSF workshop on Large-scale Random Graphs held in Budapest in 2006, at the Alfréd Rényi Institute of Mathematics, organized jointly with the University of Memphis.

Content Level » Research

Keywords » Brain Dynamics - Criticality - Graph Theory - Phase transitions - Random Graphs - Scale-free networks - Synchrony

Related subjects » Mathematics - Number Theory & Combinatorics - Theoretical Computer Science

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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)