大型網絡和圖極限拉茲洛.洛瓦茲 9787040612035 【台灣高等教育出版社】

Name: 大型網絡和圖極限 拉茲洛.洛瓦茲 9787040612035 【台灣高等教育出版社】
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書名：大型網絡和圖極限
ISBN：9787040612035
出版社：高等教育
著編譯者：拉茲洛.洛瓦茲
頁數：475
所在地：中國大陸 *此為代購商品
書號：1625009
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內容簡介

世界上許多有趣的結構和現象可以用網路來描述。發展大型網路的數學理論是重要的挑戰。本書描述了最近十年出現的新方法——圖極限理論。該理論與研究大型網路的其他方法，如計算機科學中的「性質檢驗」和圖論中的正則劃分，有著豐富的聯繫。它在極值圖論中有一些應用，包括非常普遍的問題的確切公式和部分答案，例如圖極限理論中哪些問題是可判定的。它還與數學的其他領域（經典和非經典的，如概率論、測度論、張量代數和半正定優化）有著不易察覺的聯繫。

Preface
Part 1 Large graphs: an informal introduction
Chapter 1 Very large networks
1 1 Huge networks everywhere
1 2 What to ask about them
1 3 How to obtain information about them
1 4 How to model them
1 5 How to approximate them
1 6 How to run algorithms on them
1 7 Bounded degree graphs
Chapter 2 Large graphs in mathematics and physics
2 1 Extremal graph theory
2 2 Statistical physics
Part 2 The algebra of graph homomorphisms
Chapter 3 Notation and terminology
3 1 Basic notation
3 2 Graph theory
3 3 Operations on graphs
Chapter 4 Graph parameters and connection matrices
4 1 Graph parameters and graph properties
4 2 Connection matrices
4 3 Finite connection rank
Chapter 5 Graph homomorphisms
5 1 Existence of homomorphisms
5 2 Homomorphism numbers
5 3 What hom functions can express
5 4 Homomorphism and isomorphism
5 5 Independence of homomorphism functions
5 6 Characterizing homomorphism numbers
5 7 The structure of the homomorphism set
Chapter 6 Graph algebras and homomorphism functions
6 1 Algebras of quantum graphs
6 2 Reflection positivity
6 3 Contractors and connectors
6 4 Algebras for homomorphism functions
6 5 Computing parameters with finite connection rank
6 6 The polynomial method
Part 3 Limits of dense graph sequences
Chapter 7 Kernels and graphons
7 1 Kernels， graphons and stepfunctions
7 2 Generalizing homomorphisms
7 3 Weak isomorphism I
7 4 Sums and products
7 5 Kernel operators
Chapter 8 The cut distance
8 1 The cut distance of graphs
8 2 Cut norm and cut distance of kernels
8 3 Weak and L1-topologies
Chapter 9 Szemeredi partitions
9 1 Regularity Lemma for graphs
9 2 Regularity Lemma for kernels
9 3 Compactness of the graphon space
9 4 Fractional and integral overlays
9 5 Uniqueness of regularity partitions
Chapter 10 Sampling
10 1 W-random graphs
10 2 Sample concentration
10 3 Estimating the distance by sampling
10 4 The distance of a sample from the original
10 5 Counting Lemma
10 6 Inverse Counting Lemma
10 7 Weak isomorphism II
Chapter 11 Convergence of dense graph sequences
11 1 Sampling， homomorphism densities and cut distance
11 2 Random graphs as limit objects
11 3 The limit graphon
11 4 Proving convergence
11 5 Many disguises of graph limits
11 6 Convergence of spectra
11 7 Convergence in norm
11 8 First applications
Chapter 12 Convergence from the right
12 1 Homomorphisms to the right and multicuts
12 2 The overlay functional
12 3 Right-convergent graphon sequences
12 4 Right-convergent graph sequences
Chapter 13 On the structure of graphons
13 1 The general form of a graphon
13 2 Weak isomorphism III
13 3 Pure kernels
13 4 The topology of a graphon
13 5 Symmetries of graphons
Chapter 14 The space of graphons
14 1 Norms defined by graphs
14 2 Other norms on the kernel space
14 3 Closures of graph properties
14 4 Graphon varieties
14 5 Random graphons
14 6 Exponential random graph models
Chapter 15 Algorithms for large graphs and graphons
15 1 Parameter estimation
15 2 Distinguishing graph properties
15 3 Property testing
15 4 Computable structures
Chapter 16 Extremal theory of dense graphs
16 1 Nonnegativity of quantum graphs and reflection positivity
16 2 Variational calculus of graphons
16 3 Densities of complete graphs
16 4 The classical theory of extremal graphs
16 5 Local vs global optima
16 6 Deciding inequalities between subgraph densities
16 7 Which graphs are extremal
Chapter 17 Multigraphs and decorated graphs
17 1 Compact decorated graphs
1
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