Laplacian Eigenvectors Of Graphs
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Laplacian Eigenvectors Of Graphs
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Author : Türker Biyikoglu
language : en
Publisher: Springer
Release Date : 2007-07-07
Laplacian Eigenvectors Of Graphs written by Türker Biyikoglu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-07 with Mathematics categories.
This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs.
Graph Symmetry
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Graph Symmetry written by Gena Hahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs
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Author : Jason J. Molitierno
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Applications Of Combinatorial Matrix Theory To Laplacian Matrices Of Graphs written by Jason J. Molitierno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Graphs And Matrices
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Author : Ravindra B. Bapat
language : en
Publisher: Springer
Release Date : 2014-09-19
Graphs And Matrices written by Ravindra B. Bapat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-19 with Mathematics categories.
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Spectra Of Graphs
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Author : Andries E. Brouwer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-17
Spectra Of Graphs written by Andries E. Brouwer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-17 with Mathematics categories.
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Lx B Laplacian Solvers And Their Algorithmic Applications
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Author : Nisheeth K Vishnoi
language : en
Publisher:
Release Date : 2013-03-01
Lx B Laplacian Solvers And Their Algorithmic Applications written by Nisheeth K Vishnoi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with categories.
Illustrates the emerging paradigm of employing Laplacian solvers to design novel fast algorithms for graph problems through a small but carefully chosen set of examples. This monograph can be used as the text for a graduate-level course, or act as a supplement to a course on spectral graph theory or algorithms.
Bounds For The Eigenvalues Of A Matrix
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Author : Kenneth R. Garren
language : en
Publisher:
Release Date : 1968
Bounds For The Eigenvalues Of A Matrix written by Kenneth R. Garren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Eigenvalues categories.
Graph Representation Learning
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Author : William L. Hamilton
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Graph Representation Learning written by William L. Hamilton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Computers categories.
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.
Eigenspaces Of Graphs
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Author : Dragoš M. Cvetković
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09
Eigenspaces Of Graphs written by Dragoš M. Cvetković and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-09 with Mathematics categories.
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
Graph Energy
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Author : Xueliang Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-10
Graph Energy written by Xueliang Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-10 with Mathematics categories.
This book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the conjecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an extensive coverage of recent results and a gradual development of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.