Download or read book Large Networks and Graph Limits written by László Lovász and published by American Mathematical Soc.. This book was released on 2012 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. To develop a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as ``property testing'' in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact formulations and partial answers to very general questions, such as which problems in extremal graph theory are decidable. It also has less obvious connections with other parts of mathematics (classical and non-classical, like probability theory, measure theory, tensor algebras, and semidefinite optimization). This book explains many of these connections, first at an informal level to emphasize the need to apply more advanced mathematical methods, and then gives an exact development of the theory of the algebraic theory of graph homomorphisms and of the analytic theory of graph limits. This is an amazing book: readable, deep, and lively. It sets out this emerging area, makes connections between old classical graph theory and graph limits, and charts the course of the future. --Persi Diaconis, Stanford University This book is a comprehensive study of the active topic of graph limits and an updated account of its present status. It is a beautiful volume written by an outstanding mathematician who is also a great expositor. --Noga Alon, Tel Aviv University, Israel Modern combinatorics is by no means an isolated subject in mathematics, but has many rich and interesting connections to almost every area of mathematics and computer science. The research presented in Lovasz's book exemplifies this phenomenon. This book presents a wonderful opportunity for a student in combinatorics to explore other fields of mathematics, or conversely for experts in other areas of mathematics to become acquainted with some aspects of graph theory. --Terence Tao, University of California, Los Angeles, CA Laszlo Lovasz has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks. It is an authoritative, masterful text that reflects Lovasz's position as the main architect of this rapidly developing theory. The book is a must for combinatorialists, network theorists, and theoretical computer scientists alike. --Bela Bollobas, Cambridge University, UK

Download or read book Large Networks and Graph Limits written by Làszlò Lovàsz and published by . This book was released on 2012 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large Deviations for Random Graphs written by Sourav Chatterjee and published by Springer. This book was released on 2017-08-31 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.

Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2024-02-08 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive introduction to the local and global structure of random graph models for complex networks.

Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2017 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Download or read book Network Models for Data Science written by Alan Julian Izenman and published by Cambridge University Press. This book was released on 2022-12-31 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to describe modern methods for analyzing complex networks arising from a wide range of disciplines.

Download or read book Nonlocal Continuum Limits of p Laplacian Problems on Graphs written by Imad El Bouchairi and published by Cambridge University Press. This book was released on 2023-04-30 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.

Download or read book A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree Depth written by Jaroslav Nešetřil and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.

Download or read book The Abel Prize 2018 2022 written by Helge Holden and published by Springer Nature. This book was released on 2024 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the winners of the Abel Prize in mathematics for the period 2018-2022: - Robert P. Langlands (2018) - Karen K. Uhlenbeck (2019) - Hillel Furstenberg and Gregory Margulis (2020) - Lászlo Lóvász and Avi Wigderson (2021) - Dennis P. Sullivan (2022) The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos from the period 2018-2022 showing many of the additional activities connected with the Abel Prize. This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer, 2014) as well as on The Abel Prize 2013-2017 (Springer, 2019), which profile the previous Abel Prize laureates.

Download or read book Graph Theory and Additive Combinatorics written by Yufei Zhao and published by Cambridge University Press. This book was released on 2023-07-31 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.

Download or read book Algorithms and Models for the Web Graph written by Anthony Bonato and published by Springer. This book was released on 2016-11-10 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 13th International Workshop on Algorithms and Models for the Web Graph, WAW 2016, held in Montreal, QC, Canada, in December 2016. The 13 full papers presented in this volume were carefully reviewed and selected from 14 submissions. The workshop gathered the researchers who are working on graph-theoretic and algorithmic aspects of related complex networks, including social networks, citation networks, biological networks, molecular networks, and other networks arising from the Internet.

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Holistic Analysis and Management of Distributed Social Systems written by Peter Simon Sapaty and published by Springer. This book was released on 2018-09-22 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the application of a high-level technology to solve problems in distributed systems that have networked structures with millions to billions of nodes. The main difference from other works is that the approach is based on holistically and simultaneously analysing these systems using a spatial pattern-matching mode, which produces solutions hundreds of times faster than usual. The latest version of the technology is described, together with implementation details and basic Spatial Grasp Language. In addition, the book highlights numerous solutions, covering graph and network problems, their use in large social, industrial, and business ecosystems, social robotics and driverless transport, and the possibility of extrapolating from known gestalt laws on distributed systems, which could potentially be applied in civil and defence contexts. The book is intended for system scientists, business and industry managers, economists, application programmers, security and defence personnel, as well as university students.

Download or read book Fundamentals of Computation Theory written by Leszek Antoni Gąsieniec and published by Springer. This book was released on 2019-08-01 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 22nd International Symposium on Fundamentals of Computation Theory, FCT 2019, held in Copenhagen, Denmark, in August 2019. The 21 full papers included in this volume were carefully reviewed and selected from 45 submissions. In addition, the book contains 3 invited talks in full-paper length. The papers were organized in topical sections named: formal methods, complexity, and algorithms.

Download or read book Mathematics of Epidemics on Networks written by István Z. Kiss and published by Springer. This book was released on 2017-06-08 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.

Download or read book Complex Graphs and Networks written by Fan R. K. Chung and published by American Mathematical Soc.. This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.

Download or read book The Econometric Analysis of Network Data written by Bryan Graham and published by Academic Press. This book was released on 2020-06-03 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Econometric Analysis of Network Data serves as an entry point for advanced students, researchers, and data scientists seeking to perform effective analyses of networks, especially inference problems. It introduces the key results and ideas in an accessible, yet rigorous way. While a multi-contributor reference, the work is tightly focused and disciplined, providing latitude for varied specialties in one authorial voice. Answers both 'why' and 'how' questions in network analysis, bridging the gap between practice and theory allowing for the easier entry of novices into complex technical literature and computation Fully describes multiple worked examples from the literature and beyond, allowing empirical researchers and data scientists to quickly access the 'state of the art' versioned for their domain environment, saving them time and money Disciplined structure provides latitude for multiple sources of expertise while retaining an integrated and pedagogically focused authorial voice, ensuring smooth transition and easy progression for readers Fully supported by companion site code repository 40+ diagrams of 'networks in the wild' help visually summarize key points