A First Course in Complex Networks

Complex networks are everywhere. They are increasingly important in all aspects of society. Social networks have changed the face of politics and elections. The internet of things (IoT) consisting of highway cameras, smart appliances, medical devices, and so on, is generating enormous amounts of data that fuel deep learning networks to enable autonomous control of an increasing array of physical systems. The internet and the World Wide Web have permeated all aspects of society and revolutionized communications, commerce, and finance. Thus, a course in complex networks should be part of STEM education at the undergraduate level.

This text is written for a one-semester course in complex networks for advanced undergraduate students in engineering, science, or mathematics. The book is also suitable for beginning graduate students and for self study. The intent is to present the fundamental ideas with sufficient rigor to enable further study, but without including proofs of results unless doing so adds some particular insight. I assume that the students have a basic knowledge of linear algebra, probability, and differential equations, as well as some familiarity with Matlab.

The book gives a detailed introduction to graph theory, including the adjacency and Laplacian matrices and their properties. We introduce random graphs and discuss three types of random networks, the Erdös-Rényi, small world, and scale free networks. We present various metrics for characterizing and analyzing networks, such as degree distribution, clustering, and centrality. An important feature of the book is a treatment of dynamics on networks, including epidemic models, predator-prey models, synchronization and consensus, and a short introduction to neural networks. A final chapter on chaos and fractals is included to illustrate the fractal nature of scale-free networks. Lecture slides, example problems and exams, as well as extensive Matlab code, are available from the author.