A Broad Introduction to Network Science

Network science is the field dedicated to the investigation and analysis of complex systems via their representations as networks. We normally model such networks as graphs: sets of nodes connected by sets of edges and a number of node and edge attributes. This deceptively simple object is the starting point of never-ending complexity, due to its ability to represent almost every facet of reality: chemical interactions, protein pathways inside cells, neural connections inside the brain, scientific collaborations, financial relations, citations in art history, just to name a few examples. If we hope to make sense of complex networks, we need to master a large analytic toolbox: graph and probability theory, linear algebra, statistical physics, machine learning, combinatorics, and more.

This book aims at providing the first access to all these tools. It is intended as an "Atlas", because its interest is not in making you a specialist in using any of these techniques. Rather, after reading this book, you will have a general understanding about the existence and the mechanics of all these approaches. You can use such an understanding as the starting point of your own career in the field of network science. This has been, so far, an interdisciplinary endeavor. The founding fathers of this field come from many different backgrounds: mathematics, sociology, computer science, physics, history, digital humanities, and more. This Atlas is charting your path to be something different from all of that: a pure network scientist.

The book is available for free download as a PDF using the links below or on the top bar. The website contains the exercises from each chapter of the book and their solutions. My aim is to also transform most figures from the book into interactive visualizations. By manipulating the figures you can bring about a deeper understanding of each concept.

Download | Exercise | Interact


The first edition of the book is available only as a free electronic PDF and (soon) as a print-on-demand. I am planning to expand it in a second edition and to create interactive visualizations. If you're interested in these efforts, consider supporting my work via Patreon, or buying a physical copy of the book.

Thanks to

The work on this book has been supported as a part of my professional activity as a postdoc at the Center for International Development at Harvard University, and as associate professor at the IT University of Copenhagen. It also relies on the expertise of many peer reviewers who donated their time to catch all my mistakes and omissions. The chief peer reviewer was Aaron Clauset. Special thanks go to Andres Gomez-Lievano. The other peer reviewers are, in alphabetical order: Alexey Medvedev, Andrea Tagarelli, Charlie Brummitt, Ciro Cattuto, Clara Vandeweerdt, Fred Morstatter, Giulio Rossetti, Gourab Ghoshal, Isabel Meirelles, Laura Alessandretti, Luca Rossi, Mariano Beguerisse, Marta Sales-Pardo, Matte Hartog, Petter Holme, Renaud Lambiotte, Roberta Sinatra, Yong-Yeol Ahn, and Yu-Ru Lin. Their support goes to charities: TechWomen and Evidence Action. You should consider donating to them.