TY - BOOK AU - Lovasz, Laszlo AU - Lovasz, Laszlo TI - Large Networks and Graph Limits T2 - Colloquium publications (American Mathematical Society), v. 60 SN - 9781470438364 U1 - 511.5 LOV PY - 2017/// CY - New Delhi PB - :University Press KW - Mathematics KW - General principles of mathematics KW - Graph theory KW - Combinatorics -- Graph theory -- None of the above, but in this section KW - Combinatorics -- Graph theory -- Extremal problems KW - Combinatorics -- Graph theory -- Random graphs KW - Combinatorics -- Graph theory -- Small world graphs, complex networks N1 - Large graphs: an informal introduction -- Large graphs in mathematics and physics -- Notation and terminology -- Graph parameters and connection matrices -- Graph homomorphisms -- Graph algebras and homomorphism functions -- Kernels and graphons -- The cut distance -- Szemerédi partitions -- Sampling --Convergence of dense graph sequences -- Convergence from the right -- On the structure of graphons -- The space of graphons -- Algorithms for large graphs and graphons -- Extremal theory of dense graphs -- Multigraphs and decorated graphs -- Graphings -- Convergence of bounded degree graphs --Right convergence of bounded degree graphs -- On the structure of graphings -- Algorithms for bounded degree graphs -- Other combinatorial structures N2 - "Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. Developing 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 non-classical, 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 algebraic theory of graph homomorphisms and of the analytic theory of graph limits."--Publisher description ER -