Softcover ISBN:  9780821836576 
Product Code:  CBMS/107 
List Price:  $60.00 
Individual Price:  $48.00 
eBook ISBN:  9781470424671 
Product Code:  CBMS/107.E 
List Price:  $60.00 
Individual Price:  $48.00 
Softcover ISBN:  9780821836576 
eBook: ISBN:  9781470424671 
Product Code:  CBMS/107.B 
List Price:  $120.00 $90.00 
Softcover ISBN:  9780821836576 
Product Code:  CBMS/107 
List Price:  $60.00 
Individual Price:  $48.00 
eBook ISBN:  9781470424671 
Product Code:  CBMS/107.E 
List Price:  $60.00 
Individual Price:  $48.00 
Softcover ISBN:  9780821836576 
eBook ISBN:  9781470424671 
Product Code:  CBMS/107.B 
List Price:  $120.00 $90.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 107; 2006; 264 ppMSC: Primary 05; 68; 90; 94
Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets.
How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age.
ReadershipGraduate students and research mathematicians interested in combinatorics (graph theory) and its applications to large networks.

Table of Contents

Chapters

Chapter 1. Graph theory in the information age

Chapter 2. Old and new concentration inequalities

Chapter 3. A generative model—the preferential attachment scheme

Chapter 4. Duplication models for biological networks

Chapter 5. Random graphs with given expected degrees

Chapter 6. The rise of the giant component

Chapter 7. Average distance and the diameter

Chapter 8. Eigenvalues of the adjacency matrix of $G(\mathbf {w})$

Chapter 9. The semicircle law for $G(\mathbf {w})$

Chapter 10. Coupling online and offline analyses of random graphs

Chapter 11. The configuration model for power law graphs

Chapter 12. The small world phenomenon in hybrid graphs


Additional Material

Reviews

This is a wellstructured and useful book for researchers in random graphs, combinatorics and computer science. Because of its selfcontained nature, and the careful way the topics are introduced, it is a good text for graduate level courses in the subject.
Colin D. Cooper for Mathematical Reviews


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Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets.
How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age.
Graduate students and research mathematicians interested in combinatorics (graph theory) and its applications to large networks.

Chapters

Chapter 1. Graph theory in the information age

Chapter 2. Old and new concentration inequalities

Chapter 3. A generative model—the preferential attachment scheme

Chapter 4. Duplication models for biological networks

Chapter 5. Random graphs with given expected degrees

Chapter 6. The rise of the giant component

Chapter 7. Average distance and the diameter

Chapter 8. Eigenvalues of the adjacency matrix of $G(\mathbf {w})$

Chapter 9. The semicircle law for $G(\mathbf {w})$

Chapter 10. Coupling online and offline analyses of random graphs

Chapter 11. The configuration model for power law graphs

Chapter 12. The small world phenomenon in hybrid graphs

This is a wellstructured and useful book for researchers in random graphs, combinatorics and computer science. Because of its selfcontained nature, and the careful way the topics are introduced, it is a good text for graduate level courses in the subject.
Colin D. Cooper for Mathematical Reviews