Handbook of Large-Scale Random Networks

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 descriptions 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.

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

Klappentext

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.

Inhalt
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.