Network Science

Networks pervade virtually every aspect of our lives, from how we engage with one another socially to the ways our cells interact to provide biological functionality. Networks of interacting entities can be found from the quantum world of fundamental particles to the cosmic-web structure of the known universe, and at virtually every level in between. The science of networks seeks to understand how the patterns and dynamics of interactions between the elements of a system contribute to the behavior of the system as a whole, how networks form and break down, and how they can be controlled.

Complex systems can often be represented with the help of graphs— diagrams that show discrete objects linked by a relationship, usually drawn as points with line segments between them. Mathematical graph theory goes back as far as Leonhard Euler’s solution to the puzzle of Königsberg’s bridges in 1735. However, graph theory does not equate to network science; physical network science came into being only in the past two decades. Network science is fundamentally data-centric; collecting the data that encode a map of interactions became possible only with the advent of powerful data-centric computational technology.

Once researchers looked at several real-world networks, they found surprising commonalities in the graph-theoretic properties of their representations, even for systems as seemingly disparate as the internet and protein interaction networks. Those mathematical similarities raised the possibility of common organizational principles behind the emergence of networked systems.

Network science came into existence with the goal of capturing those common principles. As a young and explosively growing field (aided by its widely interdisciplinary nature), it needs textbooks to cement its foundations. However, writing one is harder than it sounds due to the huge range of domains amenable to network analysis.

To meet the challenge, Albert-László Barabási, in his new book, Network Science, focuses on a select set of fundamental concepts that can be applied across many fields. He has written a hands-on and engaging textbook suitable for both graduate and advanced undergraduate courses.

Network Science introduces the reader to basic graph-theory notions, elements of data analysis, statistics, and some of the computational and modeling methods that allow us to interrogate network data sets. Throughout, the book illustrates those ideas with concrete and intuitive examples that also help achieve its main purpose, which is to instill network-based thinking in the reader. The writing is engaging, peppered throughout with stories, anecdotes, and historical connections.

Barabási is the director of the Center for Complex Network Research at Northeastern University and one of the founding figures of network science. He is also well known for his successful popularization Linked: The New Science of Networks (Perseus, 2002). Network Science is by no means a complete survey of everything in the field. The author makes that clear in the preface, in which he states that his choices of material are biased by his and his collaborators’ experience. Although he discusses several network measures, he centers most of the material on degree-based notions and their applications.

The book starts with Barabási’s inspirational personal history of his journey into network science. After that motivational introduction, it presents basic graph-theory concepts, followed by notions of randomness, models of random graphs, and random-graph ensembles. The following chapters focus on scale-free networks and their properties, degree correlations, and the implications of those correlations for real-world networks such as power grids and social networks.

The final three chapters of the book are particularly interesting and thought-provoking. Chapter 8, a nice exposition devoted to the question of network robustness, makes connections to percolation theory and cascading failures. Chapter 9 is devoted to the perennial issue of network communities—that is, it addresses the difficult problem of detecting clusters in networks. Communities can appear at various scales, can be node based or link based, can be overlapping, hierarchically nested, or all these at once. The last chapter both applies earlier material to the study of spreading phenomena and brings the reader up to date with the latest findings on the topic. Its discussion of the spread of disease in particular clearly illustrates the necessity of network thinking in solving a fundamental and practical problem that affects us all.

The book is carefully structured and visually pleasing, with lots of colorful diagrams, figures, tables, and schematics to help convey fundamental concepts and ideas. Its pedagogical value is significantly enhanced by a Tufte-style exposition that recognizes and works with the nonlinear character of learning. The wide margins contain bits of information—including figures, explanatory boxes, math derivations, and historical asides—that expand on the main text. When no annotations are present, the white margins invite the reader to jot down comments, questions, and observations.

Network Science is more than a book; it is also an online resource. The text is freely available at http://barabasi.com/networksciencebook in a version that includes embedded movies—for example, animations of dynamic network models. The book’s webpage contains links to software, visualization tools, data sets, data sources, and teaching materials. The book even has its own Facebook page containing additional interactive resources, discussions, edits, and news updates. Within four months of the book’s release, it was translated into Hungarian. Translations into Chinese, Japanese, Spanish, Russian, Portuguese, Italian, and German are on the way.