Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Statistical Network Analysis: Models, Issues, and New Directions held in Pittsburgh, PA, USA in June 2006 as associated event of the 23rd International Conference on Machine Learning, ICML 2006. It covers probabilistic methods for network analysis, paying special attention to model design and computational issues of learning and inference.

In recent years there has been an explosion of network data – that is, measu- ments that are either of or from a system conceptualized as a network – from se- ingly all corners of science. The combination of an increasingly pervasive interest in scienti c analysis at a systems level and the ever-growing capabilities for hi- throughput data collection in various elds has fueled this trend. Researchers from biology and bioinformatics to physics, from computer science to the information sciences, and from economics to sociology are more and more engaged in the c- lection and statistical analysis of data from a network-centric perspective. Accordingly, the contributions to statistical methods and modeling in this area have come from a similarly broad spectrum of areas, often independently of each other. Many books already have been written addressing network data and network problems in speci c individual disciplines. However, there is at present no single book that provides a modern treatment of a core body of knowledge for statistical analysis of network data that cuts across the various disciplines and is organized rather according to a statistical taxonomy of tasks and techniques. This book seeks to ll that gap and, as such, it aims to contribute to a growing trend in recent years to facilitate the exchange of knowledge across the pre-existing boundaries between those disciplines that play a role in what is coming to be called ‘network science.

David Knoke and Song Yang′s Social Network Analysis, Third Edition provides a concise introduction to the concepts and tools of social network analysis. The authors convey key material while at the same time minimizing technical complexities. The examples are simple: sets of 5 or 6 entities such as individuals, positions in a hierarchy, political offices, and nation-states, and the relations between them include friendship, communication, supervision, donations, and trade. The new edition reflects developments and changes in practice over the past decade. The authors also describe important recent developments in network analysis, especially in the fifth chapter. Exponential random graph models (ERGMs) are a prime example: when the second edition was published, P* models were the recommended approach for this, but they have been replaced by ERGMs. Finally, throughout the volume, the authors comment on the challenges and opportunities offered by internet and social media data.

Explore the multidisciplinary nature of complex networks through machine learning techniques Statistical and Machine Learning Approaches for Network Analysis provides an accessible framework for structurally analyzing graphs by bringing together known and novel approaches on graph classes and graph measures for classification. By providing different approaches based on experimental data, the book uniquely sets itself apart from the current literature by exploring the application of machine learning techniques to various types of complex networks. Comprised of chapters written by internationally renowned researchers in the field of interdisciplinary network theory, the book presents current and classical methods to analyze networks statistically. Methods from machine learning, data mining, and information theory are strongly emphasized throughout. Real data sets are used to showcase the discussed methods and topics, which include: A survey of computational approaches to reconstruct and partition biological networks An introduction to complex networks—measures, statistical properties, and models Modeling for evolving biological networks The structure of an evolving random bipartite graph Density-based enumeration in structured data Hyponym extraction employing a weighted graph kernel Statistical and Machine Learning Approaches for Network Analysis is an excellent supplemental text for graduate-level, cross-disciplinary courses in applied discrete mathematics, bioinformatics, pattern recognition, and computer science. The book is also a valuable reference for researchers and practitioners in the fields of applied discrete mathematics, machine learning, data mining, and biostatistics.

This is the first book to describe modern methods for analyzing complex networks arising from a wide range of disciplines.