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Handbook of Graphs and Networks: From the Genome to the Internet

ISBN: 978-3-527-60633-7
417 pages
March 2006
Handbook of Graphs and Networks: From the Genome to the Internet (3527606335) cover image


Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs.
This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines.
The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field.
Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

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Table of Contents


List of Contributors.

1. Mathematical Results on Scale-free Random Graphs (Béla Bollobás and Oliver Riordan).

2. Random Graphs as Models of Networks (Mark Newman).

3. Emergence of Scaling in Complex Networks (Albert-László Barabási).

4. Structural Properties of Scale-Free Networks (R. Cohen, S. Havlin, and D. ben-Avraham).

5. Epidemics and Immunization in Scale-free Networks (Romualdo Pastor-Satorras and Alessandro Vespignani).

6. Cells and Genes as Networks in Nematode Development and Evolution (Ralf J. Sommer).

7. Complex Networks in Genomics and Proteomics (Ricard V. Solé and Romualdo Pastor-Satorras).

8. Correlation Profiles and Motifs in Complex Networks (Sergei Maslov, Kim Sneppen, and Uri Alon).

9. Theory of Interacting Neural Networks (Wolfgang Kinzel).

10. Modelling Food Webs (B. Drossel and A. J. McKane).

11. Traffic Networks (Kai Nagel).

12. Economic Networks (Alan Kirman).

13. Local Search in Unstructured Networks (Lada A. Adamic, Rajan M. Lukose and Bernardo A. Huberman).

14. Accelerated Growth of Networks (S.N. Dorogovtsev and J.F.F. Mendes).

15. Social Percolators and Self Organized Criticality (Gérard Weisbuch and Sorin Solomon).

16. Graph Theory and the Evolution of Autocatalytic Networks (Sanjay Jain and Sandeep Krishna).


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Author Information

Lada A. Adamic, Uri Alon, Daniel ben-Avraham, Albert-Lásló Barabási, Béla Bollobás, Reuven Cohen, Sergei N. Dorogovtsev, Barbara Drossel, Shlomo Havlin, Bernardo A. Huberman, Sanjay Jain, Wolfgang Kinzel, Alan Kirman, Sandeep Krishna, Rajan M. Lukose, Sergei Maslov, Alan J. McKane, Jose F. F. Mendes, Kai Nagel, Mark Newman, Romualdo Pastor-Satorras, Oliver M. Riordan, Kim Sneppen, Ricard V. Solé Sorin Solomon, Ralf J. Sommer, Alessandro Vespignani, Gérard Weisbuch.

Stefan Bornholdt is Professor of Theoretical Physics and heads the Statistical Physics Group of the Interdisciplinary Center for Bioinformatics at the University of Leipzig, Germany. After studies at the University of Hamburg and UC Santa Barbara he received his doctorate in 1992. He held research positions at the Universities of Heidelberg and Kiel and in a biotech startup, and was visiting scientist at the Santa Fe Institute and the ITP Santa Barbara. His research focuses on interdisciplinary applications of theoretical and computational physics methods to complex systems in biology and other fields.

Heinz Georg Schuster is Professor of Theoretical Physics at the University of Kiel in Germany. In 1971 he attained his doctorate and in 1976 he was appointed Professor at the University of Frankfurt am Main in Germany. He was a visiting professor at the Weizmann-Institute of Science in Israel and at the California Institute of Technology in Pasadena, USA. He is author of several books, among others "Deterministic Chaos", which has been translated into five languages.

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"Die Breite der verschiednen Gesichtspunkte macht es zu einem nützlichen, wenn nicht sogar notwendigen, Hilfsmittel für alle, die auf diesem Gebiet forschen wollen." Physik Journal
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