Random graphs and complex networks. Volume 1 (Q2833172)

This book presents an updated introduction to random graphs as models for complex networks, which is a rapidly growing and extremely prolific subject nowadays. Written in a coherent and self-contained way, this book is suitable for a master level course with students having some preliminary knowledge of probability and discrete mathematics. The book (volume one) begins with an introduction in Chapter 1 giving an overall view of the key elements of random graphs and network sciences. Necessary theoretical preparations on probabilistic methods and branching processes are covered in Chapters 2 and 3, respectively, focusing on the convergence of random variables, coupling methods as well as properties of Binomial and Poisson branching processes. These results are less covered in standard textbooks on random graphs or network sciences. Erdős-Rényi random graph theory is introduced in Chapters 4 and 5, where the phase transition and the connectivity evolution are treated in detail. Most of the technical proofs are available and the results from the perspective of limit theory are fairly interesting. In the last three chapters of this volume, three relatively independent complex network models are investigated. To wit, generalized (in-homogeneous) random graphs, configuration models, and preferential attachment models. The contexts in these chapters introduce new techniques/insights, especially in the last decade, and reflect recent theoretical advances. These models are important and relevant in the modern network science and have attracted much attention from diverse areas including mathematics, physics, computer science, biology, economics and management.NEWLINENEWLINEIt is worth mentioning that the simple and readable manner in which this book is written makes it accessible reading for master level students with interdisciplinary backgrounds. Each chapter begins with the ``Organization of this Chapter'' and ends with notes and discussions, in addition to exercises, pointing to useful literature. Each exercise is provided with a running title to summarize the meaning or indicate its crux. There are many other features that make this book a special contribution. The volume two of this book detailing the models for complex networks is much expected.