The study of networks has recently achieved some prominence due to the simple fact that networks of many different kinds surround us, from social and information networks to communication and transportation networks, not to mention the biological networks that range from protein interaction networks to the neural networks behind our brain activity. As a relatively recent interdisciplinary field of study, it has attracted the attention of many researchers. Physicists, mathematicians, and computer scientists have contributed to the emergence of so-called “network science.”

The Romanian-born Hungarian-American physicist Albert-László Barabási, one of the best-known researchers in complex networks due to his work on scale-free networks starting at the end of the 20th century, is the author of this readable introduction to network science. During the last decade, many textbooks have been published that cover similar material. For instance, Vito Latora et al.’s Complex networks [1] analyzes multiple network models and some interesting topics related to network analysis, such as motif analysis and community detection. Kayhan Erciyes provides a more detailed algorithmic description of those topics [2], as does Mark Newman in his thorough textbook on networks [3]. Likewise, Ted G. Lewis’ book [4] is more practice oriented, with code examples, whereas Matthew Jackson’s Social and economic networks [5] is more academic, with a stronger emphasis on mathematical details. Barabási’s style is more informative and tries to appeal to a wider audience, closer to Easley and Kleinberg’s Networks, crowds, and markets [6].

Given the wealth of alternatives in the network science textbook market, what does Barabási offer that is not present in other books of similar scope?

First of all, a personal introduction, included as chapter 0, where he describes the ups and downs of the dawn of network science as we know it. His first papers, published in the 1990s, helped spur an interest in the then-nascent field. Obviously, graph theory has existed as a branch of mathematics since Euler solved the Königsberg bridge problem in the 18th century, whereas Erdös and Rényi proposed random graph models in 1959, yet they remained hardly known outside a small field in mathematics for four decades.

After his very personal introduction, the book covers the same topics you can easily find in any other textbook on networks. Starting with the foundations of the field, which includes the aforementioned graph theory, Barabási delves directly into network models. Separate chapters are devoted to random networks (for example, the Erdös–Rényi model), the universality of scale-free networks, the Barabási–Albert preferential attachment model, and various models of evolving networks, including, not surprisingly, the Bianconi–Barabási model. The main properties of each model are discussed, including their intuitive interpretation, practical examples, lavish illustrations, and side boxes introducing related ideas and applications. Some more advanced topics and mathematical results are provided as appendices to each chapter, so that mathematical proofs and algorithmic implementation details do not break the general flow of the text.

The final chapters of the book cover some interesting topics related to network structure and dynamics. The first one, on degree correlations, introduces the concept of assortativity (degree assortativity, to be precise): nodes of high degree, also known as hubs, tend to connect to other hubs, whereas low-degree nodes tend to connect to other small-degree nodes. Chapter 8 delves into network robustness, for example, how scale-free networks are robust to random failures, but vulnerable to targeted attacks. Chapter 9 describes community detection techniques, including hierarchical clustering, modularity optimization algorithms, and algorithms that are able to detect overlapping communities (clique percolation and link clustering, in particular). Finally, the last chapter is devoted to spreading phenomena: how networks can be used to improve epidemic modeling, immunization, and real-time epidemic prediction (not only of biological diseases, but also the spread of computer viruses or the adoption of ideas, innovations, products, behaviors, or rumors in social networks).

While all the topics included in this book are already covered elsewhere, it must be acknowledged that this textbook is clearly written, beautifully illustrated, and attractively presented to entice students. Each chapter provides some background information, covers the basics, summarizes the main results, gives pointers to key contributions in the history of the field, proposes some homework exercises, and packs in a few “advanced topics” as chapter appendices. A first-class starting point for those interested in learning about the science of networks, on par with Newman’s [3] or Easley and Kleinberg’s [6] excellent textbooks.

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