Graph Spectra for Complex Networks

Author: Piet van Mieghem
Publisher: Cambridge University Press
ISBN: 9781139492270
Release Date: 2010-12-02
Genre: Technology & Engineering

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Complex Networks

Author: B. S. Manoj
Publisher: Prentice Hall
ISBN: 9780134787121
Release Date: 2018-01-23
Genre: Computers

The Up-to-Date Guide to Complex Networks for Students, Researchers, and Practitioners Networks with complex and irregular connectivity patterns appear in biology, chemistry, communications, social networks, transportation systems, power grids, the Internet, and many big data applications. Complex Networks offers a novel engineering perspective on these networks, focusing on their key communications, networking, and signal processing dimensions. Three leading researchers draw on recent advances to illuminate the design and characterization of complex computer networks and graph signal processing systems. The authors cover both the fundamental concepts underlying graph theory and complex networks, as well as current theory and research. They discuss spectra and signal processing in complex networks, graph signal processing approaches for extracting information from structural data, and advanced techniques for multiscale analysis. What makes networks complex, and how to successfully characterize them Graph theory foundations, definitions, and concepts Full chapters on small-world, scale-free, small-world wireless mesh, and small-world wireless sensor networks Complex network spectra and graph signal processing concepts and techniques Multiscale analysis via transforms and wavelets

Analysis of Complex Networks

Author: Matthias Dehmer
Publisher: John Wiley & Sons
ISBN: 9783527627998
Release Date: 2009-07-10
Genre: Medical

Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.

Complex Graphs and Networks

Author: Fan R. K. Chung
Publisher: American Mathematical Soc.
ISBN: 9780821836576
Release Date: 2006
Genre: Computers

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.

Spectra of Graphs

Author: Andries E. Brouwer
Publisher: Springer Science & Business Media
ISBN: 9781461419396
Release Date: 2011-12-17
Genre: Mathematics

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

An Introduction to the Theory of Graph Spectra

Author: Dragoš Cvetković
Publisher: Cambridge University Press
ISBN: 0521118395
Release Date: 2009-10-15
Genre: Mathematics

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Quality of Future Internet Services

Author: Michael Smirnov
Publisher: Springer Science & Business Media
ISBN: 3540201939
Release Date: 2003-09-24
Genre: Business & Economics

This book presents a state-of-the-art survey of technologies, algorithms, models, and experiments in the area quality of Internet service. It is based on the European Action COST 263 Quality of Future Internet Services, which involved 70 researchers during a period of almost five years. The results presented in the book reflect the state of the art in the area beyond the Action COST 263. The six comprehensive chapters are written by teams of leading researchers in the area; a roadmap outlines and summarizes the overall situation and indicates future developments. The book offers chapters on traffic managements, quality of service routing, Internet traffic engineering, mobile networking, algorithms for scalable content distribution, and pricing and QoS.

Complex Networks Their Applications V

Author: Hocine Cherifi
Publisher: Springer
ISBN: 9783319509013
Release Date: 2016-12-30
Genre: Technology & Engineering

This book highlights cutting-edge research in the field of network science, offering scientists, researchers and graduate students a unique opportunity to catch up on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the fifth International Workshop on Complex Networks & their Applications (COMPLEX NETWORKS 2016), which took place in Milan during the last week of November 2016. The carefully selected papers are divided into 11 sections reflecting the diversity and richness of research areas in the field. More specifically, the following topics are covered: Network models; Network measures; Community structure; Network dynamics; Diffusion, epidemics and spreading processes; Resilience and control; Network visualization; Social and political networks; Networks in finance and economics; Biological and ecological networks; and Network analysis.

Handbook of Optimization in Complex Networks

Author: My T. Thai
Publisher: Springer Science & Business Media
ISBN: 9781461408574
Release Date: 2011-11-25
Genre: Mathematics

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In the last decade, there has been an explosive growth of research on complex real-world networks, a theme that is becoming pervasive in many disciplines, ranging from mathematics and computer science to the social and biological sciences. Optimization of complex communication networks requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network. Although there are a few books addressing social networks or complex networks, none of them has specially focused on the optimization perspective of studying these networks. This book provides the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex networks. A wide range of applications and optimization problems derived from research areas such as cellular and molecular chemistry, operations research, brain physiology, epidemiology, and ecology.

Intentional Risk Management through Complex Networks Analysis

Author: Victor Chapela
Publisher: Springer
ISBN: 9783319264233
Release Date: 2015-12-14
Genre: Mathematics

​​This book combines game theory and complex networks to examine intentional technological risk through modeling. As information security risks are in constant evolution, the methodologies and tools to manage them must evolve to an ever-changing environment. A formal global methodology is explained in this book, which is able to analyze risks in cyber security based on complex network models and ideas extracted from the Nash equilibrium. A risk management methodology for IT critical infrastructures is introduced which provides guidance and analysis on decision making models and real situations. This model manages the risk of succumbing to a digital attack and assesses an attack from the following three variables: income obtained, expense needed to carry out an attack, and the potential consequences for an attack. Graduate students and researchers interested in cyber security, complex network applications and intentional risk will find this book useful as it is filled with a number of models, methodologies and innovative examples. ​

Dynamics On and Of Complex Networks

Author: Niloy Ganguly
Publisher: Springer Science & Business Media
ISBN: 9780817647513
Release Date: 2009-06-20
Genre: Computers

This self-contained book systematically explores the statistical dynamics on and of complex networks having relevance across a large number of scientific disciplines. The theories related to complex networks are increasingly being used by researchers for their usefulness in harnessing the most difficult problems of a particular discipline. The book is a collection of surveys and cutting-edge research contributions exploring the interdisciplinary relationship of dynamics on and of complex networks. Topics covered include complex networks found in nature—genetic pathways, ecological networks, linguistic systems, and social systems—as well as man-made systems such as the World Wide Web and peer-to-peer networks. The contributed chapters in this volume are intended to promote cross-fertilization in several research areas, and will be valuable to newcomers in the field, experienced researchers, practitioners, and graduate students interested in systems exhibiting an underlying complex network structure in disciplines such as computer science, biology, statistical physics, nonlinear dynamics, linguistics, and the social sciences.

Algorithms and Discrete Applied Mathematics

Author: Sumit Ganguly
Publisher: Springer
ISBN: 9783319149745
Release Date: 2015-01-28
Genre: Computers

This book collects the refereed proceedings of the First International Conference onon Algorithms and Discrete Applied Mathematics, CALDAM 2015, held in Kanpur, India, in February 2015. The volume contains 26 full revised papers from 58 submissions along with 2 invited talks presented at the conference. The workshop covered a diverse range of topics on algorithms and discrete mathematics, including computational geometry, algorithms including approximation algorithms, graph theory and computational complexity.

Performance Analysis of Communications Networks and Systems

Author: Piet Van Mieghem
Publisher: Cambridge University Press
ISBN: 1139450824
Release Date: 2009-04-09
Genre: Technology & Engineering

This rigourous and self-contained book describes mathematical and, in particular, stochastic methods to assess the performance of networked systems. It consists of three parts. The first part is a review on probability theory. Part two covers the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory), which are considered to be the basic building blocks for performance evaluation studies. Part three focuses on the relatively new field of the physics of networks. This part deals with the recently obtained insights that many very different large complex networks - such as the Internet, World Wide Web, proteins, utility infrastructures, social networks - evolve and behave according to more general common scaling laws. This understanding is useful when assessing the end-to-end quality of communications services, for example, in Internet telephony, real-time video and interacting games. Containing problems and solutions, this book is ideal for graduate students taking courses in performance analysis.