"A Course on the Web Graph provides a comprehensive introduction to state-of-the-art research on the applications of graph theory to real-world networks such as the web graph. It is the first mathematically rigorous textbook discussing both models of the web graph and algorithms for searching the web. After introducing key tools required for the study of web graph mathematics, an overview is given of the most widely studied models for the web graph. A discussion of popular web search algorithms, e.g. PageRank, is followed by additional topics, such as applications of infinite graph theory to the web graph, spectral properties of power law graphs, domination in the web graph, and the spread of viruses in networks. The book is based on a graduate course taught at the AARMS 2006 Summer School at Dalhousie University. As such it is self-contained and includes over 100 exercises. The reader of the book will gain a working knowledge of current research in graph theory and its modern applications. In addition, the reader will learn first-hand about models of the web, and the mathematics underlying modern search engines."--Publisher's description.

This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

This book constitutes the refereed proceedings of the 8th International Workshop on Algorithms and Models for the Web-Graph, WAW 2011, held in Atlanta, GA, in May 2011 - co-located with RSA 2011, the 15th International Conference on Random Structures and Algorithms. The 13 revised full papers presented together with 1 invited lecture were carefully reviewed and selected from 19 submissions. Addressing a wide variety of topics related to the study of the Web-graph such as theoretical and empirical analysis, the papers feature original research in terms of algorithmic and mathematical analysis in all areas pertaining to the World-Wide Web with special focus to the view of complex data as networks.

This book constitutes the refereed proceedings of the 9th International Workshop on Algorithms and Models for the Web-Graph, WAW 2012, held in Halifax, Nova Scotia, Canada, in June 2012. The 13 papers presented were carefully reviewed and selected for inclusion in this volume. They address a number of topics related to the complex networks such hypergraph coloring games and voter models; algorithms for detecting nodes with large degrees; random Appolonian networks; and a sublinear algorithm for Pagerank computations.

This book constitutes the refereed proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph, WAW 2009, held in Barcelona, Spain, in February 2009 - co-located with WSDM 2009, the Second ACM International Conference on Web Search and Data Mining. The 14 revised full papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers address a wide variety of topics related to the study of the Web-graph such as theoretical and empirical analysis of the Web graph and Web 2.0 graphs, random walks on the Web and Web 2.0 graphs and their applications, and design and performance evaluation of the algorithms for social networks. The workshop papers have been naturally clustered in three topical sections on graph models for complex networks, pagerank and Web graph, and social networks and search.