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Large Networks and Graph Limits by Laszlo Lovasz
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About this book :-
Large Networks and Graph Limits written by Laszlo Lovasz
This text describes one recent approach to 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.
Book Detail :-
Title: Large Networks and Graph Limits
Author(s): Laszlo Lovasz
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Book Contents :-
Large Networks and Graph Limits written by Laszlo Lovasz cover the following topics.
Part-1 Large graphs: an informal introduction
1. Very large networks
2. Large graphs in mathematics and physics
Part-2 The algebra of graph homomorphisms
3. Notation and terminology
4. Graph parameters and connection matrices
5. Graph homomorphisms
6. Graph algebras and homomorphism functions
Part-3 Limits of dense graph sequences
7. Kernels and graphons
8. The cut distance
9. Szemer´edi partitions
11. Convergence of dense graph sequences
12. Convergence from the right
13. On the structure of graphons
14. The space of graphons
15. Algorithms for large graphs and graphons
16. Extremal theory of dense graphs
17. Multigraphs and decorated graphs
Part-4 Limits of bounded degree graphs
19. Convergence of bounded degree graphs
20. Right convergence of bounded degree graphs
21. On the structure of graphings
22. Algorithms for bounded degree graphs
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