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.

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.

Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.

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.

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.

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.

Provides the mathematical, stochastic and graph theoretic methods to analyse the performance and robustness of complex networks and systems.