Graphs

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Graph Representation Learning

Author : William L. William L. Hamilton
Publisher : Springer Nature
Page : 141 pages
File Size : 46,7 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031015885

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Graph Representation Learning by William L. William L. Hamilton Pdf

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.

Introduction to Graph Theory

Author : Koh Khee Meng,Dong Fengming,Tay Eng Guan
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 46,9 Mb
Release : 2007-03-15
Category : Mathematics
ISBN : 9789813101630

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Introduction to Graph Theory by Koh Khee Meng,Dong Fengming,Tay Eng Guan Pdf

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

Strongly Regular Graphs

Author : Andries E. Brouwer,H. Van Maldeghem
Publisher : Unknown
Page : 481 pages
File Size : 43,8 Mb
Release : 2022-01-13
Category : Language Arts & Disciplines
ISBN : 9781316512036

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Strongly Regular Graphs by Andries E. Brouwer,H. Van Maldeghem Pdf

This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.

Introduction to Random Graphs

Author : Alan Frieze,Michał Karoński
Publisher : Cambridge University Press
Page : 483 pages
File Size : 45,9 Mb
Release : 2016
Category : Mathematics
ISBN : 9781107118508

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Introduction to Random Graphs by Alan Frieze,Michał Karoński Pdf

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Making Graphs

Author : Bridget Heos
Publisher : Math World
Page : 0 pages
File Size : 54,6 Mb
Release : 2015-08
Category : Juvenile Nonfiction
ISBN : 1622432355

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Making Graphs by Bridget Heos Pdf

A class is learning a lesson on making graphs and interpreting data, and the class clown, Logan, has some off-the-wall answers to his classmates' surveys.

Graphs and Geometry

Author : László Lovász
Publisher : American Mathematical Soc.
Page : 444 pages
File Size : 43,7 Mb
Release : 2019-08-28
Category : Geometry
ISBN : 9781470450878

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Graphs and Geometry by László Lovász Pdf

Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This book surveys a number of such connections between graph theory and geometry: among others, rubber band representations, coin representations, orthogonal representations, and discrete analytic functions. Applications are given in information theory, statistical physics, graph algorithms and quantum physics. The book is based on courses and lectures that the author has given over the last few decades and offers readers with some knowledge of graph theory, linear algebra, and probability a thorough introduction to this exciting new area with a large collection of illuminating examples and exercises.

Symmetry in Graphs

Author : Ted Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Cambridge University Press
Page : 527 pages
File Size : 47,7 Mb
Release : 2022-05-12
Category : Language Arts & Disciplines
ISBN : 9781108429061

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Symmetry in Graphs by Ted Dobson,Aleksander Malnič,Dragan Marušič Pdf

The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Handbook of Graph Theory

Author : Jonathan L. Gross,Jay Yellen
Publisher : CRC Press
Page : 1200 pages
File Size : 44,8 Mb
Release : 2003-12-29
Category : Computers
ISBN : 0203490207

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Handbook of Graph Theory by Jonathan L. Gross,Jay Yellen Pdf

The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach

Functions and Graphs

Author : I. M. Gelfand,E. G. Glagoleva,E. E. Shnol
Publisher : Courier Corporation
Page : 112 pages
File Size : 49,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780486317137

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Functions and Graphs by I. M. Gelfand,E. G. Glagoleva,E. E. Shnol Pdf

This text demonstrates the fundamentals of graph theory. The 1st part employs simple functions to analyze basics; 2nd half deals with linear functions, quadratic trinomials, linear fractional functions, power functions, rational functions. 1969 edition.

Graphs

Author : Sara Pistoia,Piper Whelan
Publisher : Unknown
Page : 24 pages
File Size : 52,9 Mb
Release : 2019
Category : Graph theory
ISBN : 1510545603

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Graphs by Sara Pistoia,Piper Whelan Pdf

Introduces graphs by sorting and counting objects and comparing them with bar and line graphs.

Graph Grammars and Their Application to Computer Science

Author : Janice Cuny
Publisher : Springer Science & Business Media
Page : 582 pages
File Size : 55,9 Mb
Release : 1996-05-08
Category : Computers
ISBN : 3540612289

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Graph Grammars and Their Application to Computer Science by Janice Cuny Pdf

This book describes the functional properties and the structural organization of the members of the thrombospondin gene family. These proteins comprise a family of extracellular calcium binding proteins that modulate cellular adhesion, migration and proliferation. Thrombospondin-1 has been shown to function during angiogenesis, wound healing and tumor cell metastasis.

Knowledge Graphs

Author : Aidan Hogan,Eva Blomqvist,Michael Cochez,Claudia d’Amato,Gerard de Melo,Claudio Gutierrez,Sabrina Kirrane,Jose Emilio Labra Gayo,Roberto Navigli,Sebastian Neumaier,Axel Polleres,Sabbir Rashid,Anisa Rula,Antoine Zimmermann,Lukas Schmelzeisen,Axel-Cyrille Ngonga Ngomo,Juan Sequeda,Steffen Staab
Publisher : Springer Nature
Page : 247 pages
File Size : 47,9 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031019180

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Knowledge Graphs by Aidan Hogan,Eva Blomqvist,Michael Cochez,Claudia d’Amato,Gerard de Melo,Claudio Gutierrez,Sabrina Kirrane,Jose Emilio Labra Gayo,Roberto Navigli,Sebastian Neumaier,Axel Polleres,Sabbir Rashid,Anisa Rula,Antoine Zimmermann,Lukas Schmelzeisen,Axel-Cyrille Ngonga Ngomo,Juan Sequeda,Steffen Staab Pdf

This book provides a comprehensive and accessible introduction to knowledge graphs, which have recently garnered notable attention from both industry and academia. Knowledge graphs are founded on the principle of applying a graph-based abstraction to data, and are now broadly deployed in scenarios that require integrating and extracting value from multiple, diverse sources of data at large scale. The book defines knowledge graphs and provides a high-level overview of how they are used. It presents and contrasts popular graph models that are commonly used to represent data as graphs, and the languages by which they can be queried before describing how the resulting data graph can be enhanced with notions of schema, identity, and context. The book discusses how ontologies and rules can be used to encode knowledge as well as how inductive techniques—based on statistics, graph analytics, machine learning, etc.—can be used to encode and extract knowledge. It covers techniques for the creation, enrichment, assessment, and refinement of knowledge graphs and surveys recent open and enterprise knowledge graphs and the industries or applications within which they have been most widely adopted. The book closes by discussing the current limitations and future directions along which knowledge graphs are likely to evolve. This book is aimed at students, researchers, and practitioners who wish to learn more about knowledge graphs and how they facilitate extracting value from diverse data at large scale. To make the book accessible for newcomers, running examples and graphical notation are used throughout. Formal definitions and extensive references are also provided for those who opt to delve more deeply into specific topics.

Introduction to Quantum Graphs

Author : Gregory Berkolaiko,Peter Kuchment
Publisher : American Mathematical Soc.
Page : 291 pages
File Size : 46,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821892114

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Introduction to Quantum Graphs by Gregory Berkolaiko,Peter Kuchment Pdf

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Chemical Graph Theory

Author : D Bonchev
Publisher : CRC Press
Page : 310 pages
File Size : 48,8 Mb
Release : 1991-01-01
Category : Science
ISBN : 0856264547

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Chemical Graph Theory by D Bonchev Pdf

Initiates an ongoing series intended to consider a wide range of topics related to the mathematics of chemistry. Presents the fundamentals of graph theory and specific chemical applications of its. The topics include historical background, basic ideas and mathematical formalism, graph theory's influence in the rationalization of chemical nomenclature, graph-theoretical polynomials, and the interplay with molecular orbital theory in terms of graph spectral theory and topological resonance. Suitable for advanced undergraduates, graduates, and professionals. Acidic paper. Book club price, $52. Annotation copyrighted by Book News, Inc., Portland, OR

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke,Robin J. Wilson,Peter J. Cameron
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,7 Mb
Release : 2004-10-04
Category : Mathematics
ISBN : 9781107079458

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Topics in Algebraic Graph Theory by Lowell W. Beineke,Robin J. Wilson,Peter J. Cameron Pdf

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.