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.