Graph Spectra For Complex Networks

Download or read book Graph Spectra for Complex Networks written by Piet van Mieghem and published by Cambridge University Press. This book was released on 2010-12-02 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Graph Spectra for Complex Networks written by Piet Van Mieghem and published by Cambridge University Press. This book was released on 2023-09-21 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and self-contained introduction builds up the spectral theory of graphs from scratch, including linear algebra and the theory of polynomials. Covering several types of graphs, it provides the mathematical foundation needed to understand and apply spectral insight to real-world communications systems and complex networks.

Download or read book An Introduction to the Theory of Graph Spectra written by Dragoš Cvetković and published by Cambridge University Press. This book was released on 2009-10-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Spectra of Graphs written by Dragoš M. Cvetković and published by . This book was released on 1980 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.

Download or read book Graph Theory and Complex Networks written by Maarten van Steen and published by Maarten Van Steen. This book was released on 2010 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks. In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they: 1.Have learned how to read and understand the basic mathematics related to graph theory. 2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks. 3.Know a bit more about this sometimes mystical field of small worlds and random networks. There is an accompanying web site www.distributed-systems.net/gtcn from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks.

Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2017 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Download or read book Modularity and Dynamics on Complex Networks written by Renaud Lambiotte and published by Cambridge University Press. This book was released on 2022-02-03 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.