Offers a comprehensive overview of random graphs and networks
Emphasis on modelling complex real-world networks such as brains, biological and physical memories, computer systems and communication
New conjectures are outlined and new directions for future research are defined
A link is established between the fundamental mathematical, graph theoretical approach and the approach based on methods of statistical physics
Contains a detailed methodological deillegalscription of various applications, such as reaction-diffusion equations, cellular regulation and intracellular networks, neural networks and brain networks, social networks, telecommunication and learning behaviors in networks
With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the "Handbook of Graphs and Networks” published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
Part I: Theoretical FoundationsChapter 1 Random graphs and branching processesBela Bollobas and Oliver Riordan (Cambridge University, UK)Chapter 2 Sentry Selection in wireless networksPaul Balister and Bela Bollobas (U of Memphis, TN, and Cambridge University, UK) Amites Sarkar and Mark WaltersChapter 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 systemsChapter 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 societyChapter 9 k-clique percolation and clusteringGergely 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 netsGabor 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 LemmaAndras 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)
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.
From the reviews:
"It is a collection of papers on advances in the field of large-scale networks ... . The material presented here is based on a workshop organized in Budapest in 2006. ... An ideal reader of the book may be a mathematician ... .” (Miklós Bóna, The Mathematical Association of America, February, 2010)
"The volume is an outcome of a U.S.-Hungarian workshop on complex networks held at the Rényi Istitute in Budapest in 2006. ... I quite enjoyed reading the book. The choice of topics and presentations is illustrative of the type of work taking place in this area ... . are likely to be useful to the theoretical computer scientist interested in random structures and algorithms, but most of the chapters were reasonably interesting to me.” (Gabriel Istrate, SIGACT News, April, 2012)
Based on material from the 2006 NSF workshop on Large-scale Random Graphs, this book describes recent advances made in large scale networks. It includes detailed deillegalscriptions of various applications and explores areas for future research.
With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the "Handbook of Graphs and Networks" published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
Random Graphs and Branching Processes.- Percolation, Connectivity, Coverage and Colouring of Random Geometric Graphs.- Scaling Properties of Complex Networks and Spanning Trees.- Random Tree Growth with Branching Processes - A Survey.- Reaction-diffusion Processes in Scale-free Networks.- Toward Understanding the Structure and Function of Cellular Interaction Networks.- Scale-Free Cortical Planar Networks.- Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity.- k-Clique Percolation and Clustering.- The Inverse Problem of Evolving Networks - with Application to Social Nets.- Learning and Representation: From Compressive Sampling to the 'Symbol Learning Problem'.- Telephone Call Network Data Mining: A Survey with Experiments.
From the reviews:
"It is a collection of papers on advances in the field of large-scale networks ... . The material presented here is based on a workshop organized in Budapest in 2006. ... An ideal reader of the book may be a mathematician ... ." (Miklós Bóna, The Mathematical Association of America, February, 2010)
"The volume is an outcome of a U.S.-Hungarian workshop on complex networks held at the Rényi Istitute in Budapest in 2006. ... I quite enjoyed reading the book. The choice of topics and presentations is illustrative of the type of work taking place in this area ... . are likely to be useful to the theoretical computer scientist interested in random structures and algorithms, but most of the chapters were reasonably interesting to me." (Gabriel Istrate, SIGACT News, April, 2012)
Inhaltsverzeichnis
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)
Klappentext
With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the "Handbook of Graphs and Networks" published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
Offers a comprehensive overview of random graphs and networks
rn
Emphasis on modelling complex real-world networks such as brains, biological and physical memories, computer systems and communication
rn
New conjectures are outlined and new directions for future research are defined
rn
A link is established between the fundamental mathematical, graph theoretical approach and the approach based on methods of statistical physics
rn
Contains a detailed methodological deillegalscription of various applications, such as reaction-diffusion equations, cellular regulation and intracellular networks, neural networks and brain networks, social networks, telecommunication and learning behaviors in networks
rn
