Graph Theory(Reinhard Diestel).pdf

This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses

Python星 这是python中的简单实现 文献资料 astar模块定义了AStar类，该类必须继承并完成以下几种方法的实现： 邻居 @ abstractmethod def neighbors ( self , node ) 对于给定的节点，返回（或产生）其邻居列表。 此方法必须在子类中实现 这是一种为了向算法提供图形描述以供计算时使用的方法 此方法必须在子类中实现。 之间的距离 @ abstractmethod def distance_between ( self , n1 , n2 ) 给出两个相邻节点n1和n2之间的实际距离/成本（即n2属于n1邻居的列表）。 保证n2属于通过调用近邻（n1）返回的列表。 此方法必须在子类中实现。 heuristic_cost_estimate @ abstractmethod def heuristic_cost_estimat

Graph Theory Authors: Adrian Bondy, U.S.R Murty Publisher: Springer; 3rd Corrected Printing edition (Aug 14 2008) ISBN-10: 1846289696 ISBN-13: 978-1846289699 = Product Description = The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory. = Table of Contents = Graphs - Subgraphs - Connected Graphs - Trees - Separable and Nonseparable Graphs - Tree-Search Algorithms - Flows in Networks - Complexity of Algorithms - Connectivity - Planar Graphs - The Four-Colour Problem - Stable Sets and Cliques - The Probabilistic Method - Vertex Colourings - Colourings of Maps - Matchings - Edge Colourings - Hamilton Cycles - Coverings and Packings in Directed Graphs - Electrical Networks - Integer Flows and Coverings - Unsolved Problems - References - Glossary - Index = Reviews = For more than three decades, the authors' Graph Theory with Applications (1976) has served as perhaps the classic introduction to graph theory. With happy shock, the reader learns that Bondy and Murty have updated the book, doubling its size. Three decades would count as a long time in the life of any active scientific pursuit, but the original year of publication saw the solution to the four-color conjecture that catalyzed a vast revitalization of graph theory. Graph theory, moreover, now has intimate interactions with computer science, practical and theoretical: three decades ago, computer networks barely existed and the founding papers of complexity theory had just appeared. Connections between graph theory and probability have also undergone a revolution. In short, the passage of time has transformed this subject in these and other ways, and the authors have transformed their book accordingly. They do, by choice, largely omit the theory of graph minors (developed by Paul Seymour and Neil Robertson and followers), which certainly now deserves a monographic treatment of its own. Summing up: Recommended. Lower-division undergraduate through professional collections. CHOICE This book is a follow-on to the authors' 1976 text, Graphs with Applications. What began as a revision has evolved into a modern, first-class, graduate-level textbook reflecting changes in the discipline over the past thirty years... This text hits the mark by appearing in Springer’s Graduate Texts in Mathematics series, as it is a very rigorous treatment, compactly presented, with an assumption of a very complete undergraduate preparation in all of the standard topics. While the book could ably serve as a reference for many of the most important topics in graph theory, it fulfills the promise of being an effective textbook. The plentiful exercises in each subsection are divided into two groups, with the second group deemed "more challenging". Any exercises necessary for a complete understanding of the text have also been marked as such. There is plenty here to keep a graduate student busy, and any student would learn much in tackling a selection of the exercises... Not only is the content of this book exceptional, so too is its production. The high quality of its manufacture, the crisp and detailed illustrations, and the uncluttered design complement the attention to the typography and layout. Even in simple black and white with line art, it is a beautiful book. SIAM Book Reviews "A text which is designed to be usable both for a basic graph theory course … but also to be usable as an introduction to research in graph theory, by including more advanced topics in each chapter. There are a large number of exercises in the book … . The text contains drawings of many standard interesting graphs, which are listed at the end." (David B. Penman, Zentralblatt MATH, Vol. 1134 (12), 2008) MathSciNet Reviews "The present volume is intended to serve as a text for "advanced undergraduate and beginning graduate students in mathematics and computer science" (p. viii). It is well suited for this purpose. The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging… Even a complete listing of the chapters does not fully convey the breadth of this book… For researchers in graph theory, this book offers features which parallel the first Bondy and Murty book: it provides well-chosen terminology and notation, a multitude of especially interesting graphs, and a substantial unsolved problems section…One-hundred unsolved problems are listed in Appendix A, a treasure trove of problems worthy of study… (In short) this rewrite of a classic in graph theory stands a good chance of becoming a classic itself." "The present volume is intended to serve as a text for ‘advanced undergraduate and beginning graduate students in mathematics and computer science’ … . The writing is fully accessible to the stated groups of students, and indeed is not merely readable but is engaging. The book has many exercise sets, each containing problems … ." (Arthur M. Hobbs, Mathematical Reviews, Issue 2009 C) "A couple of fantastic features: Proof techniques: I love these nutshelled essences highlighted in bordered frames. They look like pictures on the wall and grab the view of the reader. Exercises: Their style, depth and logic remind me of Lovász’ classical exercise book. Also the fact that the name of the author is bracketed after the exercise…Figures: Extremely precise and high-tech…The book contains very recent results and ideas. It is clearly an up-to-date collection of fundamental results of graph theory…All-in-all, it is a marvelous book." (János Barát, Acta Scientiarum Mathematicarum, Vol. 75, 2009)

The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and combinatorial optimization. Divided into 11 cohesive sections, the handbook’s 44 chapters focus on graph theory, combinatorial optimization, and algorithmic issues. The book provides readers with the algorithmic and theoretical foundations to: Understand phenomena as shaped by their graph structures Develop needed algorithmic and optimization tools for the study of graph structures Design and plan graph structures that lead to certain desirable behavior With contributions from more than 40 worldwide experts, this handbook equips readers with the necessary techniques and tools to solve problems in a variety of applications. Readers gain exposure to the theoretical and algorithmic foundations of a wide range of topics in graph theory and combinatorial optimization, enabling them to identify (and hence solve) problems encountered in diverse disciplines, such as electrical, communication, computer, social, transportation, biological, and other networks. Table of Contents SECTION I - Basic Concepts and Algorithms CHAPTER 1 - Basic Concepts in Graph Theory and Algorithms CHAPTER 2 - Basic Graph Algorithms CHAPTER 3 - Depth-First Search and Applications SECTION II - Flows in Networks CHAPTER 4 - Maximum Flow Problem CHAPTER 5 - Minimum Cost Flow Problem CHAPTER 6 - Multicommodity Flows SECTION III - Algebraic Graph Theory CHAPTER 7 - Graphs and Vector Spaces CHAPTER 8 - Incidence, Cut, and Circuit Matrices of a Graph CHAPTER 9 - Adjacency Matrix and Signal Flow Graphs CHAPTER 10 - Adjacency Spectrum and the Laplacian Spectrum of a Graph CHAPTER 11 - Resistance Networks, Random Walks, and Network Theorems SECTION IV - Structural Graph Theory CHAPTER 12 - Connectivity CHAPTER 13 - Connectivity Algorithms CHAPTER 14 - Graph Connectivity Augmentation CHAPTER 15 - Matchings CHAPTER 16 - Matching Algorithms CHAPTER 17 - Stable Marriage Problem CHAPTER 18 - Domination in Graphs CHAPTER 19 - Graph Colorings SECTION V - Planar Graphs CHAPTER 20 - Planarity and Duality CHAPTER 21 - Edge Addition Planarity Testing Algorithm CHAPTER 22 - Planarity Testing Based on PC-Trees CHAPTER 23 - Graph Drawing SECTION VI - Interconnection Networks CHAPTER 24 - Introduction to Interconnection Networks CHAPTER 25 - Cayley Graphs CHAPTER 26 - Graph Embedding and Interconnection Networks SECTION VII - Special Graphs CHAPTER 27 - Program Graphs CHAPTER 28 - Perfect Graphs CHAPTER 29 - Tree-Structured Graphs SECTION VIII - Partitioning CHAPTER 30 - Graph and Hypergraph Partitioning SECTION IX - Matroids CHAPTER 31 - Matroids CHAPTER 32 - Hybrid Analysis and Combinatorial Optimization SECTION X - Probabilistic Methods, Random Graph Models, and Randomized Algorithms CHAPTER 33 - Probabilistic Arguments in Combinatorics CHAPTER 34 - Random Models and Analyses for Chemical Graphs CHAPTER 35 - Randomized Graph Algorithms: Techniques and Analysis SECTION XI - Coping with NP-Completeness CHAPTER 36 - General Techniques for Combinatorial Approximation CHAPTER 37 - ε-Approximation Schemes for the Constrained Shortest Path Problem CHAPTER 38 - Constrained Shortest Path Problem: Lagrangian Relaxation-Based Algorithmic Approaches CHAPTER 39 - Algorithms for Finding Disjoint Paths with QoS Constraints CHAPTER 40 - Set-Cover Approximation CHAPTER 41 - Approximation Schemes for Fractional Multicommodity Flow Problems CHAPTER 42 - Approximation Algorithms for Connectivity Problems CHAPTER 43 - Rectilinear Steiner Minimum Trees CHAPTER 44 - Parameter Algorithms and Complexity

在许多实际的数据挖掘应用程序中，例如文本分类，可以轻松获得未加标签的训练示例，但获得加标签的训练示例则相当昂贵。 因此，半监督学习算法引起了数据挖掘和机器学习领域的极大兴趣。 近年来，基于图的半监督学习已成为半监督学习社区中最活跃的研究领域之一。 本文提出了一种基于线性邻域模型的新颖的基于图的半监督学习方法，该方法假设每个数据点都可以从其邻域进行线性重构。 我们的算法称为线性邻域传播（LNP），可以使用这些线性邻域以足够的平滑度将标签从标记点传播到整个数据集。 本文对LNP的性质进行了理论分析。 此外，我们还导出了一种简单的方法来将LNP扩展到样本外数据。 对于合成数据，数字和文本分类任务，提出了有希望的实验结果。

用C++或者C写复杂网络的相关程序是比较好的 因为Java或者Matlab在处理大规模网络时的运算速度真是太慢~~

关于图论的理论与应用，学习网络，计算机的好书。考研，找工作都可以。

Reinhard Diestel牛人的图论英文教材第3版（2005），已经解密。

J.A. Bondy和U.S.R. Murty著的《Graph Theory with Application》(Elsevier,1976)是图论教材中的经典，时至今日，仍不失为初学者较好的入门书。还记得兰州交通大学的张忠辅教授说过，国内第一届图论学会就是把大家集中起来学习邦迪的《Graph Theory with Application》，由此可见这本书对国内图论届的影响是如此之大。