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Handbook of Large-Scale Random Networks

  • Book
  • © 2008

Overview

Editors:
  1. Béla Bollobás

    1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, UK
      Dept. Mathematical Sciences, University of Memphis, Memphis, USA

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  2. Robert Kozma

    1. Dept. Mathematical Sciences, University of Memphis, Memphis, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Dezső Miklós

    1. Alfréd Rényi Inst. of Mathematics, Budapest, Hungary

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    You can also search for this editor in PubMed   Google Scholar

  • 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 description 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

Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 18)

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Table of contents (12 chapters)

  1. Front Matter

    Pages 1-14
    Download chapter PDF

  2. Random Graphs and Branching Processes

    • Béla Bollobás, Oliver Riordan
    Pages 15-115

  3. Percolation, Connectivity, Coverage and Colouring of Random Geometric Graphs

    • Paul Balister, Amites Sarkar, Béla Bollobás
    Pages 117-142

  4. Scaling Properties of Complex Networks and Spanning Trees

    • Reuven Cohen, Shlomo Havlin
    Pages 143-169

  5. Random Tree Growth with Branching Processes — A Survey

    • Anna Rudas, Bálint Tóth
    Pages 171-202

  6. Reaction-diffusion Processes in Scale-free Networks

    • Michele Catanzaro, Marián Boguñá, Romualdo Pastor-Satorras
    Pages 203-237

  7. Toward Understanding the Structure and Function of Cellular Interaction Networks

    • Juilee Thakar, Claire Christensen, Réka Albert
    Pages 239-275

  8. Scale-Free Cortical Planar Networks

    • Walter J. Freeman, Robert Kozma, Béla Bollobá, Oliver Riordan
    Pages 277-324

  9. Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

    • Tamás Nepusz, László Négyessy, Gábor Tusnády, Fülöp Bazsó
    Pages 325-368

  10. k-Clique Percolation and Clustering

    • Gergely Palla, Dániel Ábel, Illés J. Farkas, Péter Pollner, Imre Derényi, Tamás Vicsek
    Pages 369-408

  11. The Inverse Problem of Evolving Networks — with Application to Social Nets

    • Gábor Csárdi, Katherine J. Strandburg, Jan Tobochnik, Péter Érdi
    Pages 409-443

  12. Learning and Representation: From Compressive Sampling to the ‘Symbol Learning Problem’

    • András Lőrincz
    Pages 445-488

  13. Telephone Call Network Data Mining: A Survey with Experiments

    • Miklós Kurucz, László Lukács, Dávid Silklói, András A. Benczúr, Károly Csalogány, András Lukács
    Pages 489-530

  14. Back Matter

    Pages 531-538
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Keywords

About this book

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.

Reviews

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)

Editors and Affiliations

  • Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, UK

    Béla Bollobás

  • Dept. Mathematical Sciences, University of Memphis, Memphis, USA

    Béla Bollobás, Robert Kozma

  • Alfréd Rényi Inst. of Mathematics, Budapest, Hungary

    Dezső Miklós

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