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.

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.

This book presents a perspective of network analysis as a tool to find and quantify significant structures in the interaction patterns between different types of entities. Moreover, network analysis provides the basic means to relate these structures to properties of the entities. It has proven itself to be useful for the analysis of biological and social networks, but also for networks describing complex systems in economy, psychology, geography, and various other fields. Today, network analysis packages in the open-source platform R and other open-source software projects enable scientists from all fields to quickly apply network analytic methods to their data sets. Altogether, these applications offer such a wealth of network analytic methods that it can be overwhelming for someone just entering this field. This book provides a road map through this jungle of network analytic methods, offers advice on how to pick the best method for a given network analytic project, and how to avoid common pitfalls. It introduces the methods which are most often used to analyze complex networks, e.g., different global network measures, types of random graph models, centrality indices, and networks motifs. In addition to introducing these methods, the central focus is on network analysis literacy – the competence to decide when to use which of these methods for which type of question. Furthermore, the book intends to increase the reader's competence to read original literature on network analysis by providing a glossary and intensive translation of formal notation and mathematical symbols in everyday speech. Different aspects of network analysis literacy – understanding formal definitions, programming tasks, or the analysis of structural measures and their interpretation – are deepened in various exercises with provided solutions. This text is an excellent, if not the best starting point for all scientists who want to harness the power of network analysis for their field of expertise.

Network thinking and network analysis are rapidly expanding features of ecological research. Network analysis of ecological systems include representations and modelling of the interactions in an ecosystem, in which species or factors are joined by pairwise connections. This book provides an overview of ecological network analysis including generating processes, the relationship between structure and dynamic function, and statistics and models for these networks. Starting with a general introduction to the composition of networks and their characteristics, it includes details on such topics as measures of network complexity, applications of spectral graph theory, how best to include indirect species interactions, and multilayer, multiplex and multilevel networks. Graduate students and researchers who want to develop and understand ecological networks in their research will find this volume inspiring and helpful. Detailed guidance to those already working in network ecology but looking for advice is also included.

This is the first textbook on social network analysis integrating theory, applications, and professional software for performing network analysis. The book introduces the main concepts and their applications in social research with exercises. An application section explaining how to perform the network analyses with Pajek software follows each theoretical section.

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.