This chapter is from the book
This chapter is from the book
This chapter is from the book
1.6 Organization of the Book
This chapter (Chapter 1) introduced the topics covered by the textbook, such as applications and the emerging relevance to complex networks.
Chapter 2 provides a preliminary discussion on graph theoretical foundations, which are necessary for grasping the rest of this book. While graph theory is an established area, we provide only the necessary elements required for understanding and appreciating complex networks topics.
Chapter 3 provides an introduction to complex networks where various examples and applications of real-world complex networks are discussed. This chapter serves as the introduction to the core areas covered by the book. A detailed discussion of the foundations of random networks is also provided in Chapter 3. Mathematical models corresponding to random networks and the estimated characteristics of random networks are essential topics covered in this chapter.
Small-world networks and their characteristics are presented in Chapter 4. Many real-world networks that are categorized as small-world networks and their key characteristics, such as APL, ACC, and other relevant properties, are presented. Many techniques used for creating small-world networks out of regular networks are also presented in this chapter.
Chapter 5 covers one of the most popular and interesting complex networks called scale-free networks. Scale-free networks are present in many natural and man-made physical world networks. In many examples of real-world networks, the evolutionary characteristics required for formation of scale-free networks are discussed in detail in Chapter 5.
Some of the applications of the small-world networks can be seen in wireless networks such as WMNs. Chapter 6 covers the use of small-world concepts in WMNs to create SWWMNs. SWWMNs benefit from performance improvement, low APL, and efficiency in resource management. This chapter also classifies the existing approaches for creating SWWMNs.
Similar to SWWMNs, another application area of small-world networking in wireless networking is WSNs. WSNs are used for monitoring and control of environmental parameters in large-scale sensor fields where sensor devices, which are tiny, inexpensive, and capable of sensing many physical world parameters, are deployed. Such WSNs benefit from application of small-world concepts for performance improvement. Chapter 7 presents benefits of using SWWSNs, challenges in designing them, existing techniques for transforming a WSN to SWWSN, and a set of open research issues.
Chapters 8 through 11 deal with the spectral analysis of complex networks and graph signal processing. Chapter 8 presents the eigenvalues and eigenvectors of various matrices related to a graph or a complex network. This chapter also serves as a preliminary to graph signal processing.
Chapter 9 discusses analysis and processing of data defined on complex networks, known as graph signals. Representations of graph signals have complex and irregular structures that require novel processing techniques, which has led to the emerging field of graph signal processing as discussed in Chapter 9.
Chapter 10 presents existing approaches for graph signal processing. There are mainly two frameworks for graph signal processing. The first method is based on the (symmetric) Laplacian matrix of the graph. The second method, known as the discrete signal processing on graphs (DSPG) framework, is rooted in the algebraic signal processing theory and based on the graph shift operator. Both of these frameworks are discussed in detail in Chapter 10.
Chapter 11 presents multiscale transforms for complex network data analysis. Wavelet transforms have the capability to simultaneously localize a signal content in both time and frequency that allows us to extract information from the data at various scales. This chapter presents various techniques for multiscale analysis of complex networks.
1.6.1 Suggested Navigation for Contents of the Book
Figure 1.4 shows the navigation flow of the chapters of this book. The introductory chapters (Chapters 1–3) provide the basics to understand the rest of the book. These chapters offer a motivation for the study of complex networks. Chapter 2 provides fundamentals of graph theory. Chapter 3 provides a brief technical introduction to complex networks. Those who are familiar with graph theory and its fundamentals can skip Chapter 2 and proceed to Chapter 3.
)
Figure 1.4 Suggested navigation sequence for contents of the book
After reading Chapters 1, 2, and 3, a reader may take two major directions: (i) complex networks and (ii) graph signal processing. Chapters 4 and 5 cover small-world networks and scale-free networks. After having some foundations of small-world networks, a reader may proceed to reading in the direction of computer networks where many applications of small-world approaches in wireless networks are presented, including SWWMNs and SWWSNs.
Computer scientists may read through Chapters 3 and 4, before focusing on Chapters 6 and 7.
After Chapter 3, a reader may also proceed to Chapters 8 through 11 that present the graph signal processing approaches for various complex networks. Readers who are familiar with complex networks and who want to understand graph signal processing concepts can read Chapters 8 through 11 straightaway.
While each chapter is written in a self-contained manner, the textbook provides necessary references to the required topics present in other chapters as well as those in research literature. Therefore, reading any chapter individually is not difficult.
