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Product Description
The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form. ... Read more

Customer Reviews (2)

dense monograph
Sadly the authors have opted for a level
of abstraction that obscures many of the
beautiful details.Particularly disappointing
is the last chapter on matrix theory which veers
off into an odd mixture of marginalia which have
almost no applications.

An excellent treatise on applied combinatorics.
This book is an excellent resource for mathematicians, computer scientists, and engineers.The book shows how to use zero-one matrices and stochastic matrices in your work.The text pretty shows a lot ofinteresting properties different matrices have and how to compute variousvalues associated with graphs from them.The book would be very useful forpeople interested in Neural Networks, Speech Recognition, ArtificialIntelligence.It is mathematics, though and it describes the properties ofthe matrices and contains many proofs about these properties.Make surethat you have mastered linear algebra and combinatorics before reading thistext. ... Read more

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The book is intended to be an introductory text formathematics and computer science students at the second and third yearlevel in universities. It gives an introduction to the subject withsufficient theory for that level of student, with emphasis onalgorithms and applications. ... Read more

Customer Reviews (3)

Answer key?
I am working on this book on my own. There are a number of errors, even in the first chapter. I'm surprised, given that the book has had five reprintings! Is there an errata sheet available? How about an answer key? These errors make the book difficult to work with without a teacher.

A suitable text for an undergraduate course
This book seems to be one of the best choices of the text for an undergraduate course. It covers all topics that can be included in such course. It contains many exercises. Some of the exercises are routine, some others are more challenging. Also the price of the paperback edition is quite reasonable for a text for a semester course.
I should mention that there are some misprints in this text. Also, there are some gaps in the proof of the Brooks' theorem (pp. 194-196). So a new corrected printing is desirable.

A First Look at Graph Theory
Deseo este libr ... Read more

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"Brown is well known for research on mathematical modeling in the social sciences. His book introduces the graph algebra approach to modeling systems in the social sciences."

-CHOICE

Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied.

Key Features:

• Designed for readers in the social sciences with minimal mathematical training: In this volume, the author assists readers in developing their own difference and differential equation model specifications
• Incorporates Social Theory: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated algebraic statements of social and political phenomena. Graph algebra can be used to algebraically “flesh-out” even the most complicated and sophisticated of theories.
• Contains social science examples of graph algebra models: Social science readers can see many examples of how graph algebra can be used to model theories from a wide variety of substantive areas and disciplines. The book also describes how to estimate such models, and two examples are fully worked out.
• Explains linear and nonlinear model specifications using graph algebra from a social science perspective: Readers can move beyond simple linear regression models by using graph algebra.

This text is ideal for use in graduate courses such as Statistical Modeling, Quantitative Methods, and Applied Mathematics.

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Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics.

New to the Fifth Edition

• New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings
• New examples, figures, and applications to illustrate concepts and theorems
• Expanded historical discussions of well-known mathematicians and problems
• More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book
• Reorganization of sections into subsections to make the material easier to read
• Bolded definitions of terms, making them easier to locate

Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.

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With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material.The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica. ... Read more

Customer Reviews (3)

useful for who want to learn discrete mathematics with mathematica of Wolfram research software
though the program created more than 6 years ago, it's useful reference for learning discrete mathematics with mathematica software

Way too specialized to be a stand alone discrete math text
I think the best parts of this book was the illustration overleafs for each chapter. There are some pretty cool images created using Combinatorica and Mathematica. I got this book to help me with my Discrete math course and with that in mind it wasn't as helpful as I thought it would be. I think the reason is that it's really a book about Combinatorica and how to use it with Mathematica and how the latest version is faster and how the functions were written. So in order to use it effectively you have to already be quite familiar with discrete math and graph theory to use this. There are plenty of examples to try and play with though if you can get it to run. In Mathematica7 and I would get alot of this command is obsolete warnings or errors. The book website says they have an updated version of Combinatorica but I didn't try that. Also, there are some exercises but no answers provided for any of them. There is also a complete listing of all the Combinatorica in the book but no clear indication if it's now included with the latest version of Mathematica which would be helpful. I don't see how this book could be used as a primary text for a discrete math course unless you had an excellent instructor to add all the material the book is missing and to walk you though putting the example in the book to best use. This book will appeal most to those that use Mathematica with discrete math and find the documentation lacking or want to find out how the Combinatorica functions were programmed. If you are using it just to supplement a discrete math course as I did you probably won't benefit as much.
I must admit it was kind fun seeing Mathematica choke up on trying to spit out a 20x20 gridgraph! Never seen it do that before on my quadcore pc.

It fills a Mathematica niche to perfection
This book has two primary uses, as a reference for the Combinatorica extension to Mathematica or as a textbook in a course in combinatorics and graph theory where Mathematica is extensively used. In both cases it is the best resource on the market. Combinatorica is an extremely powerful package that allows for very sophisticated operations to be performed in combinatorics and on graphs. However, there is no coverage of other areas of discrete mathematics.
The structure of the book is that it is split up into sections. For each section, there is a short textual description of the operation, a section of code illustrating the appropriate function(s) and the output from that code. The output is sometimes in the form of a textual listing and at other times an actual diagram. A complete listing of the functions and their actions is given in an appendix.
While this book is not one that could be used in a general course in discrete mathematics, it is an exceptional example of one that fills a niche to perfection. If you have any interest in doing combinatoric or graphing operations with Mathematica, then you have to look no further.

Published in Journal of Recreational Mathematics, reprinted with permission.
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Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) “Geometric” properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.

The volume investigates the structure of eigenvectors and looks at the number of their sign graphs (“nodal domains”), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.

Product Description
This is a companion to the book Introduction to Graph Theory (World Scientific, 2006). The student who has worked on the problems will find the solutions presented useful as a check and also as a model for rigorous mathematical writing. For ease of reference, each chapter recaps some of the important concepts and/or formulae from the earlier book. ... Read more

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This book is designed to describe fundamentalalgorithmic techniques for constructing drawings of graphs. Suitable as a book or reference manual, its chapters offer anaccurate, accessible reflection of the rapidly expanding field of graphdrawing. ... Read more

Customer Reviews (7)

The best book I can find on the topic, but not really that good
I'm giving this book 4 stars only because it is dramatically better than the other books that are available on this topic.If there were better competition I would give it 3 stars since it has a range of flaws.The major flaw has been mentioned by other reviewers; it gives only terse and highly mathematical descriptions of the algorithms and the effort to convert anything in this book into an actual algorithm is huge.However on the plus side, the book is mostly well written and is actually much *less* mathematical than almost every other book on the topic.Most other planar graph drawing books just lay down some formulas and assume implementation is obvious (very far from true in this topic).However, this book does at least give a nod to the algorithm side and lays out a general framework for an implementation of most of the important layout types.The book also gives a strong foundation for almost the entire field; probably because the authors represent some of the strongest contributors to this field.So the bottom line is that, as of today you almost have to buy this book if you want to work on this type of software since no other book comes close to explaining as much and does it as well as this book.

Graph drawing, 1st edition
Worth reading, if a little dated now. These guys all know their stuff, as one would expect from such distinguished writers in the field. Can't wait for the second edition.

Not the best book ever...
This graph drawing book is, according to my lecturer, one of the few books on this subject. There is a different book too, written by some japanese authors. The drawback of the latter book is that it is too technical sometimes, while this book discusses intuitively understandable algorithms.
But, there are also some major drawbacks concerning this book. Not all chapters are equally good: some are horrible to read while others are very understandable.
Furthermore, the book is not printed anymore, so you just purchase a black-and-white copy of the original book with some fancy cover. Since the book is just copied, some pictures do not look like the way they should and one picture isn't shown at all. This results in some difficulties understanding the pictures and discussed material. I purchased one of the cheaper variants of the book, maybe the more expensive ones are printed versions.
Also, the book is absolutely not free of mistakes!
To conclude: the book is probably OK for understanding the basics of graph drawing, considering what's for sale. But beware of the drawbacks of this book and use it with care.

Who is this book for?
I am a mathematician/computer scientist quite interested in the subject matter, but the book is almost useless, since it mostly discusses ad hoc methods, and avoids proving any of the actual theorems in the subject. Unfortunate, since there is certainly room for a good book on the subject.

Not useful for me, maybe for other people
To me the book is not useful, because I need to draw graphs in which the distance between two connected vertices is fixed. The book doesn't mention any method to handle graphs with such a restriction, although the chapter on force-directed methods inspired me to use something similar. If you draw graphs without that restriction, the book might be useful to you - that's why I'm careful and give it 4 stars.

I disagree with Viv. R who said it doesn't contain pseudo code, because the book contains quite some of it, though not in every chapter. But even lack of pseudo code doesn't bother me, because for an experienced mathematical programmer that should be no problem. ... Read more

Product Description
This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study. ... Read more

Customer Reviews (2)

Standard reference in the subject
And has a lot of material, but the organization leaves much to be desired, and standard results in the field are there but very difficult to find (for example, good luck finding the proof of the classical Erdos-Renyi theorem on connectivity threshold for random graphs. The canonical proof is about half a page, while the proof you can back out of Bollobas is maybe two chapters. The configuration model (which is actually due to the author) is actually very simple and explained well in papers by N. Wormald. It is a little painful to read about in this book. Perhaps the most widely used property of random graphs is that they have the expander property (another result of Erdos). This is also carefully hidden.

It is also a little painful for me to give a less than glowing review of this, since I really like Modern Graph Theory, and random graphs are pervasive in modern mathematics, so we really need a good book. This one is not bad, but...

Written by a Master in the Field
This is the second book by Dr. Bollobas that I have read, and it is clear, that Dr. Bollobas is a master in the field.
It is amazing, how few lines he needs to motivate the subject matter completely.
The gaps in the proofs were sometimes large for me, but then again, the audience he wishes to address are "research students and professional mathematicians", and I am only a hobby mathematician.

The only minus point are the large number of misprints: I counted over 130 of them, and this is not counting misprints like 'some' instead of 'same', etc. This is very annoying if one uses the book for self study.

(Unfortunaltely misprints seem Dr. Bollobas' problem: Also the other book I read: 'Modern Graph Theory' had more than its share)


... Read more

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Primarily of interest to researchers interested in graph theory from mathematics, combinatorics, computer science and telecommunications. The book will also appeal to students of graph theory. ... Read more

Customer Reviews (1)

For advanced undergraduate students and above
This is not a friendly book in any sense of the word.I didn't find it as cohesive as I imagined it to be.It contains a somewhat random smattering of important original papers about perfect graphs.I used this book as a source for my thesis, and I expected to get more out of it than I did.I ended up only using history from it because it was too advanced for me.I am a senior undergraduate math major with only 1/3 of a semester's experience in graph theory, in an easycombinatorics class.I'm sure someone with more experience will find this book much more useful. ... Read more

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This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications.The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions.The final part of the book presents the tools of "modern" set theory: Martin's Axiom, the Diamond Principle, and elements of forcing.Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields. ... Read more

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Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem.

Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

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Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.

This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.

With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.

Product Description
Covers an enormous scope of information, with extensive treatment of searching and advanced data structures, sorting, string processing, computational geometry, graph problems, and mathematical algorithms. Provides clear and relevant insight into why the algorithms work. Softcover.Amazon.com Review
Robert Sedgewick's Algorithms series has earned a place amongthe classics of computer books. Algorithms in C++ provides acomprehensive collection of classic algorithms for sorting, searching,parsing, geometrical manipulation, and more. The book includes notjust C++ code but detailed--yet readable--explanations of how it worksand what each algorithm's advantages and disadvantages are in terms ofexecution time and memory demands. An invaluable and timelessresource. ... Read more

Customer Reviews (34)

Terse
It's quite terse and needs many more COMPLETE diagrams for better visualization of difficult concepts. Fill-in-the-details sort of diagrams don't quite cut it for understanding complicated algorithms. The explanation of code isn't that verbose, so you might have to read the same sentence three or more times to understand its meaning.

Brilliant book on Graphs and Graph Algorithms!
I am not going to give you an amazing review here. All I can do is help "up" the score of this book, because it has been lowered by other reviews which are not even reviews of previous editions of this book (there are none!). Actually, several (if not most), are of this nature. Others are even worse, for they are reviews of previous editions of Parts I-IV, for the version in C! The new 3rd edition for the first volume is much better, and the book featured in this page: Volume II of Sedgewick's Algorithms in C++, is really good too.

Just a few things I want to say:
-The book is not hard to read (I am an Ecuadorian, living in Ecuador, first language is Spanish, and even then, I can understand the author very well).
-The explanations are amazing. Not only that, but Sedgewick really gives you loads of insight on all the topics covered.
-Even with little mathematical content, one can understand rather well the complexity of all algorithms (and data structure implementations) in this book.
-Perfect as a Reference. Sections are small, and one can jump in at any time.
-Plenty of (incredible) exercises
-Implementations are actually very good, very readable. Sure, the Author may not have the best of programming practices, but any reader programming in C++ should read Effective C++ anyways. If you dislike the fact that variables are often not given the best of names, rest assured that the author, more often than not, explains their nature.

Plain average!
This is an okay book. The algorithms are described in great detail (actually sometimes too much detail), moreover it is not very mathematical. For this reason it could be the choice for the readers fed up of the math in other algorithms books e.g., Cormen et al's.

However the biggest complain I have with this book is that it is overloaded with too much contents. When things could have been described in a few lines, dozens of paragraphes have been used for it. The reader just losts in the text. And interestingly the job is still not done, i.e., the reader is still not able to follow the algorithms easily.

Also for this reason it is not a good choice for someone wants to get a quick overview or revision.

Bought this to complete the series...
I don't intend to read this book from front to back (well maybe one day if I get really bored) but I think this book does a very good job explaining the algorithm without getting obsessed with overly formal mathematical games.In my opinion the graphs are the most important part of the series, since these are the algorithms and data structures that usually AREN'T included in a programming language's libraries; STL for example.You will find many of these topics in a mathematics and statistics program (how I first encountered them) so the book does get mathematical, but out of necessity.

4 out of 5 stars for sometimes being unclear.

Best of thebunch
I had to teach this course and must see it is the pick of the books I have seen on this subject though it is far from ideal. Why can't these people use meaningful variable names and comment the code. Is it the authors intent to teach bad programming practice. ... Read more

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This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. ... Read more

Customer Reviews (1)

An excellent book
My special field is neither statistics nor math. My reading this book was for research purpose. I enjoyed reading it, though it contains a few of "printing" mistakes.

The chapter 6 is somehow hard-to-find. Ibelieve Talagrand's isoperimetric theory has wide range of applications.But it is not easy to read his original article (which, besides, is morethan 100-page long). The chapter gives a very informative introduction tothe theory. ... Read more

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This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Product Description
Graphs are extremely useful in modelling systems in physical sciences and engineering problems, because of their intuitive diagrammatic nature. This text gives a reasonably deep account of material closely related to engineering applications. Topics like directed-graph solutions of linear equations, topological analysis of linear systems, state equations, rectangle dissection and layouts, and minimal cost flows are included. A major theme of the book is electrical network theory. This book is basically intended as a reference text for researchers, and requires a certain level of mathematical maturity. However the text may equally well be used for graduate level courses on network topology and linear systems and circuits. Some of the later chapters are suitable as topics for advanced seminars. A special feature of the book is that references to other published literature are included for almost all the results presented, making the book handy for those wishing to continue with a study of special topics. ... Read more

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Graph theory is an important branch of contemporary combinatorial mathematics.By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs 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 labeling 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.Current research on these topics is part of a wider effort to forge closer links between algebra and combinatorics. 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. ... Read more