The book integrates approaches from mathematics, physics and computer sciences to analyse the organisation of complex networks. Every organisational principle of networks is defined, quantified and then analysed for its influences on the properties and functions of molecular, biological, ecological and social networks.

Filling a gap in literature, this self-contained book presents theoretical and application-oriented results that allow for a structural exploration of complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Applications to biology, chemistry, linguistics, and data analysis are emphasized. The book is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. It may also be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.

This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.

Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.

Community structure is a salient structural characteristic of many real-world networks. Communities are generally hierarchical, overlapping, multi-scale and coexist with other types of structural regularities of networks. This poses major challenges for conventional methods of community detection. This book will comprehensively introduce the latest advances in community detection, especially the detection of overlapping and hierarchical community structures, the detection of multi-scale communities in heterogeneous networks, and the exploration of multiple types of structural regularities. These advances have been successfully applied to analyze large-scale online social networks, such as Facebook and Twitter. This book provides readers a convenient way to grasp the cutting edge of community detection in complex networks. The thesis on which this book is based was honored with the “Top 100 Excellent Doctoral Dissertations Award” from the Chinese Academy of Sciences and was nominated as the “Outstanding Doctoral Dissertation” by the Chinese Computer Federation.

A comprehensive introduction to the theory and applications of complex network science, complete with real-world data sets and software tools.