About the Cover

The center image on the cover represents an artistic design composed of fractal grid structures as a metaphor for digital business, science, communications, and technology.

The technical drawing at the top left on the cover is a representation of a 40-node string topology network (STN) that is transformed to an average path length (APL)-optimal small-world network after the addition of six long-range links (LLs) with the greedy global decision based LL addition technique. Due to the greedy LL addition, most of the LLs are attached to one of the anchor points that gradually evolves to a hub-node due to the long-range link affinity (see Section 5.10 for more details), and thus, the small-world network gradually evolves to a scale-free network. The anchor points can be found at the 0.2N^th and 0.8N^th fractional locations in an N-node STN (see Section 4.8 for more details) and can serve many purposes, such as a gateway to the Internet, an energy-resourceful node in an emergency response network deployment, and a controller node for vehicle-to-vehicle communication in a platoon.

The three small graphs on the top right of the cover represent the eigenvectors of the Laplacian matrix for the five-node graph; u₀ is the eigenvector corresponding to the smallest magnitude eigenvalue and u₄ is the eigenvector corresponding to the largest magnitude eigenvalue. The variations in the eigenvectors of the graph Laplacian with respect to the network topology increase with the increase in the corresponding eigenvalue magnitudes. This simple but powerful property allows us to perform frequency analysis of signals defined on complex networks and, subsequently, paves the way for sampling theory and multiscale analysis of complex network data (see Chapter 11). The equation L_inu = λu defines the eigenvector u for directed (in-degree) Laplacian matrix L_in of an arbitrary graph, and λ is the corresponding eigenvalue. Details can be found in Chapter 10.