Large networks and graph limits
 Author/Creator
 Lovász, László, 1948
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2012]
 Copyright notice
 ©2012
 Physical description
 xiv, 475 pages : illustrations ; 26 cm
 Series
 Colloquium publications (American Mathematical Society) ; v. 60.
Access
Available online

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QA1 .A5225 V.60

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QA1 .A5225 V.60
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Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Publisher's Summary
 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 nonclassical, 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Graph theory.
 Algebra, Abstract.
 Combinatorics  Graph theory  None of the above, but in this section.
 Combinatorics  Graph theory  Graphs and abstract algebra (groups, rings, fields, etc.)
 Combinatorics  Graph theory  Extremal problems.
 Combinatorics  Graph theory  Random graphs.
 Combinatorics  Graph theory  Small world graphs, complex networks.
 Combinatorics  Graph theory  Graph algorithms.
 Operations research, mathematical programming  Operations research and management science  Network models, stochastic.
Bibliographic information
 Publication date
 2012
 Copyright date
 2012
 Responsibility
 László Lovász.
 Series
 American Mathematical Society colloquium publications ; volume 60
 ISBN
 9780821890851 (alk. paper)
 0821890859 (alk. paper)