Large networks and graph limits:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2012
|
| Schriftenreihe: | American Mathematical Society: Colloquium publications
60 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 451 - 463 |
| Beschreibung: | XIV, 475 S. Diagramme |
| ISBN: | 9780821890851 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040925354 | ||
| 003 | DE-604 | ||
| 005 | 20221111 | ||
| 007 | t | ||
| 008 | 130404s2012 xxu|||| |||| 00||| eng d | ||
| 010 | |a 2012034211 | ||
| 020 | |a 9780821890851 |c alk. paper |9 978-0-8218-9085-1 | ||
| 035 | |a (OCoLC)829219388 | ||
| 035 | |a (DE-599)BVBBV040925354 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-188 |a DE-20 |a DE-83 |a DE-739 | ||
| 050 | 0 | |a QA166 | |
| 082 | 0 | |a 511/.5 | |
| 084 | |a SK 170 |0 (DE-625)143221: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a 05Cxx |2 msc | ||
| 084 | |a 58J35 |2 msc | ||
| 084 | |a 94Cxx |2 msc | ||
| 100 | 1 | |a Lovász, László |d 1948- |e Verfasser |0 (DE-588)108767337 |4 aut | |
| 245 | 1 | 0 | |a Large networks and graph limits |c László Lovász |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2012 | |
| 300 | |a XIV, 475 S. |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: Colloquium publications |v 60 | |
| 500 | |a Literaturverz. S. 451 - 463 | ||
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Algebra, Abstract | |
| 650 | 7 | |a Combinatorics -- Graph theory -- None of the above, but in this section |2 msc | |
| 650 | 7 | |a Combinatorics -- Graph theory -- Graphs and abstract algebra (groups, rings, fields, etc.) |2 msc | |
| 650 | 7 | |a Combinatorics -- Graph theory -- Extremal problems |2 msc | |
| 650 | 7 | |a Combinatorics -- Graph theory -- Random graphs |2 msc | |
| 650 | 7 | |a Combinatorics -- Graph theory -- Small world graphs, complex networks |2 msc | |
| 650 | 7 | |a Combinatorics -- Graph theory -- Graph algorithms |2 msc | |
| 650 | 7 | |a Operations research, mathematical programming -- Operations research and management science -- Network models, stochastic |2 msc | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Isomorphismus |0 (DE-588)4143978-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 1 | |a Isomorphismus |0 (DE-588)4143978-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1583-9 |
| 830 | 0 | |a American Mathematical Society: Colloquium publications |v 60 |w (DE-604)BV035417609 |9 60 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025904409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025904409 | ||
Datensatz im Suchindex
| _version_ | 1804150222013595648 |
|---|---|
| adam_text | Titel: Large networks and graph limits
Autor: Lovász, László
Jahr: 2012
Contents
Preface xi
Part 1. Large graphs: an informai introduction 1
Chapter I. Very large networks 3
1.1. Huge networks everywhere 3
1.2. What to ask about them? 4
1.3. How to obtain information about them? 5
1.4. How to model them? 8
1.5. How to approximate them? 11
1.6. How to run algorithms on them? 18
1.7. Bounded degree graphs 22
Chapter 2. Large graphs in mathematics and physics 25
2.1. Extremal graph theory 25
2.2. Statistical physics 32
Part 2. The algebra of graph homomorphisms 35
Chapter 3. Notation and terminology 37
3.1. Basic notation 37
3.2. Graph theory 38
3.3. Operations on graphs 39
Chapter 4. Graph parameters and connection matrices 41
4.1. Graph parameters and graph properties 41
4.2. Connection matrices 42
4.3. Finite connection rank 45
Chapter 5. Graph homomorphisms 55
5.1. Existence of homomorphisms 55
5.2. Homomorphism numbers 56
5.3. What hom functions can express 62
5.4. Homomorphism and isomorphism 68
5.5. Independence of homomorphism functions 72
5.6. Characterizing homomorphism numbers 75
5.7. The structure of the homomorphism set 79
Chapter 6. Graph algebras and homomorphism functions 83
6.1. Algebras of quantum graphs 83
6.2. Reflection positivity 88
viii CONTENTS
6.3. Contractors and connectors 94
6.4. Algebras for homomorphism functions 101
6.5. Computing parameters with finite connection rank 106
6.6. The polynomial method 108
Part 3. Limits of dense graph sequences 113
Chapter 7. Kernels and graphons 115
7.1. Kernels, graphons and stepfunctions 115
7.2. Generalizing homomorphisms 116
7.3. Weak isomorphism I 121
7.4. Sums and products 122
7.5. Kernel operators 124
Chapter 8. The cut distance 127
8.1. The cut distance of graphs 127
8.2. Cut norm and cut distance of kernels 131
8.3. Weak and Li-topologies 138
Chapter 9. Szemerédi partitions 141
9.1. Regularity Lemma for graphs 141
9.2. Regularity Lemma for kernels 144
9.3. Compactness of the graphon space 149
9.4. Fractional and integral overlays 151
9.5. Uniqueness of regularity partitions 154
Chapter 10. Sampling 157
10.1. W-random graphs 157
10.2. Sample concentration 158
10.3. Estimating the distance by sampling 160
10.4. The distance of a sample from the original 164
10.5. Counting Lemma 167
10.6. Inverse Counting Lemma 169
10.7. Weak isomorphism II 170
Chapter 11. Convergence of dense graph sequences 173
11.1. Sampling, homomorphism densities and cut distance 173
11.2. Random graphs as limit objects 174
11.3. The limit graphon 180
11.4. Proving convergence 185
11.5. Many disguises of graph limits 193
11.6. Convergence of spectra 194
11.7. Convergence in norm 196
11.8. First applications 197
Chapter 12. Convergence from the right 201
12.1. Homomorphisms to the right and multicuts 201
12.2. The overlay functional 205
12.3. Right-convergent graphon sequences 207
12.4. Right-convergent graph sequences 211
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
CONTENTS ix
Chapter 13. On the structure of graphons 217
13.1. The general form of a graphon 217
220
222
225
234
239
239
242
247
250
256
259
Chapter 15. Algorithms for large graphs and graphons 263
15.1. Parameter estimation 263
15.2. Distinguishing graph properties 266
15.3. Property testing 268
15.4. Computable structures 276
Chapter 16. Extremal theory of dense graphs 281
16.1. Nonnegativity of quantum graphs and reflection positivity 281
16.2. Variational calculus of graphons 283
16.3. Densities of complete graphs 285
16.4. The classical theory of extremal graphs 293
16.5. Local vs. global optima 294
16.6. Deciding inequalities between subgraph densities 299
16.7. Which graphs are extremal? 307
Chapter 17. Multigraphs and decorated graphs 317
17.1. Compact decorated graphs 318
17.2. Multigraphs with unbounded edge multiplicities 325
Part 4. Limits of bounded degree graphs 327
Chapter 18. Graphings 329
18.1. Borel graphs 329
18.2. Measure preserving graphs 332
18.3. Random rooted graphs 338
18.4. Subgraph densities in graphings 344
18.5. Local equivalence 346
18.6. Graphings and groups 349
Chapter 19. Convergence of bounded degree graphs 351
19.1. Local convergence and limit 351
19.2. Local-global convergence 360
Chapter 20. Right convergence of bounded degree graphs 367
20.1. Random homomorphisms to the right 367
20.2. Convergence from the right 375
x CONTENTS
Chapter 21. On the structure of graphings 383
21.1. Hyperfiniteness 383
21.2. Homogeneous decomposition 393
Chapter 22. Algorithms for bounded degree graphs 397
22.1. Estimable parameters 397
22.2. Testable properties 402
22.3. Computable structures 405
Part 5. Extensions: a brief survey 413
Chapter 23. Other combinatorial structures 415
23.1. Sparse (but not very sparse) graphs 415
23.2. Edge-coloring models 416
23.3. Hypergraphs 421
23.4. Categories 425
23.5. And more... 429
Appendix A. Appendix 433
A.I. Möbius functions 433
A.2. The Tutte polynomial 434
A.3. Some background in probability and measure theory 436
A.4. Moments and the moment problem 441
A.5. Ultraproduct and ultralimit 444
A.6. Vapnik-Chervonenkis dimension 445
A.7. Nonnegative polynomials 446
A.8. Categories 447
Bibliography 451
Author Index 465
Subject Index 469
Notation Index 473
|
| any_adam_object | 1 |
| author | Lovász, László 1948- |
| author_GND | (DE-588)108767337 |
| author_facet | Lovász, László 1948- |
| author_role | aut |
| author_sort | Lovász, László 1948- |
| author_variant | l l ll |
| building | Verbundindex |
| bvnumber | BV040925354 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166 |
| callnumber-search | QA166 |
| callnumber-sort | QA 3166 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 890 |
| ctrlnum | (OCoLC)829219388 (DE-599)BVBBV040925354 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02552nam a2200589 cb4500</leader><controlfield tag="001">BV040925354</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20221111 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130404s2012 xxu|||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2012034211</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821890851</subfield><subfield code="c">alk. paper</subfield><subfield code="9">978-0-8218-9085-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)829219388</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040925354</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA166</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.5</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 170</subfield><subfield code="0">(DE-625)143221:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">05Cxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">58J35</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">94Cxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lovász, László</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)108767337</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Large networks and graph limits</subfield><subfield code="c">László Lovász</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Math. Soc.</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 475 S.</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">American Mathematical Society: Colloquium publications</subfield><subfield code="v">60</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 451 - 463</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Graph theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra, Abstract</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- None of the above, but in this section</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- Graphs and abstract algebra (groups, rings, fields, etc.)</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- Extremal problems</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- Random graphs</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- Small world graphs, complex networks</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Combinatorics -- Graph theory -- Graph algorithms</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Operations research, mathematical programming -- Operations research and management science -- Network models, stochastic</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Isomorphismus</subfield><subfield code="0">(DE-588)4143978-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Isomorphismus</subfield><subfield code="0">(DE-588)4143978-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1583-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">American Mathematical Society: Colloquium publications</subfield><subfield code="v">60</subfield><subfield code="w">(DE-604)BV035417609</subfield><subfield code="9">60</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025904409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025904409</subfield></datafield></record></collection> |
| id | DE-604.BV040925354 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:35:29Z |
| institution | BVB |
| isbn | 9780821890851 |
| language | English |
| lccn | 2012034211 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025904409 |
| oclc_num | 829219388 |
| open_access_boolean | |
| owner | DE-188 DE-20 DE-83 DE-739 |
| owner_facet | DE-188 DE-20 DE-83 DE-739 |
| physical | XIV, 475 S. Diagramme |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Colloquium publications |
| series2 | American Mathematical Society: Colloquium publications |
| spelling | Lovász, László 1948- Verfasser (DE-588)108767337 aut Large networks and graph limits László Lovász Providence, RI American Math. Soc. 2012 XIV, 475 S. Diagramme txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Colloquium publications 60 Literaturverz. S. 451 - 463 Graph theory Algebra, Abstract Combinatorics -- Graph theory -- None of the above, but in this section msc Combinatorics -- Graph theory -- Graphs and abstract algebra (groups, rings, fields, etc.) msc Combinatorics -- Graph theory -- Extremal problems msc Combinatorics -- Graph theory -- Random graphs msc Combinatorics -- Graph theory -- Small world graphs, complex networks msc Combinatorics -- Graph theory -- Graph algorithms msc Operations research, mathematical programming -- Operations research and management science -- Network models, stochastic msc Graphentheorie (DE-588)4113782-6 gnd rswk-swf Isomorphismus (DE-588)4143978-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Isomorphismus (DE-588)4143978-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1583-9 American Mathematical Society: Colloquium publications 60 (DE-604)BV035417609 60 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025904409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lovász, László 1948- Large networks and graph limits American Mathematical Society: Colloquium publications Graph theory Algebra, Abstract Combinatorics -- Graph theory -- None of the above, but in this section msc Combinatorics -- Graph theory -- Graphs and abstract algebra (groups, rings, fields, etc.) msc Combinatorics -- Graph theory -- Extremal problems msc Combinatorics -- Graph theory -- Random graphs msc Combinatorics -- Graph theory -- Small world graphs, complex networks msc Combinatorics -- Graph theory -- Graph algorithms msc Operations research, mathematical programming -- Operations research and management science -- Network models, stochastic msc Graphentheorie (DE-588)4113782-6 gnd Isomorphismus (DE-588)4143978-8 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4143978-8 |
| title | Large networks and graph limits |
| title_auth | Large networks and graph limits |
| title_exact_search | Large networks and graph limits |
| title_full | Large networks and graph limits László Lovász |
| title_fullStr | Large networks and graph limits László Lovász |
| title_full_unstemmed | Large networks and graph limits László Lovász |
| title_short | Large networks and graph limits |
| title_sort | large networks and graph limits |
| topic | Graph theory Algebra, Abstract Combinatorics -- Graph theory -- None of the above, but in this section msc Combinatorics -- Graph theory -- Graphs and abstract algebra (groups, rings, fields, etc.) msc Combinatorics -- Graph theory -- Extremal problems msc Combinatorics -- Graph theory -- Random graphs msc Combinatorics -- Graph theory -- Small world graphs, complex networks msc Combinatorics -- Graph theory -- Graph algorithms msc Operations research, mathematical programming -- Operations research and management science -- Network models, stochastic msc Graphentheorie (DE-588)4113782-6 gnd Isomorphismus (DE-588)4143978-8 gnd |
| topic_facet | 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 Graphentheorie Isomorphismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025904409&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417609 |
| work_keys_str_mv | AT lovaszlaszlo largenetworksandgraphlimits |