Networks an introduction
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2011
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| Ausgabe: | Reprinted three times |
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| 100 | 1 | |a Newman, Mark E. J. |e Verfasser |0 (DE-588)133013073 |4 aut | |
| 245 | 1 | 0 | |a Networks |b an introduction |c M. E. J. Newman |
| 250 | |a Reprinted three times | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2011 | |
| 300 | |a XI, 772 S., IV Taf. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Computer networks / Mathematics | |
| 650 | 4 | |a Social networks / Mathematics | |
| 650 | 4 | |a Mathematik | |
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| adam_text |
Contents
Preface x
1
Introduction
1
1 The empirical study of networks
15
2
Technological networks
17
2.1
The Internet
. 18
2.2
The telephone network
. 28
2.3
Power grids
. 31
2.4
Transportation networks
. 32
2.5
Delivery and distribution networks
. 33
3
Social networks
36
3.1
The empirical study of social networks
. 36
3.2
Interviews and questionnaires
. 39
3.3
Direct observation
. 46
3.4
Data from archival or third-party records
. 47
3.5
Affiliation networks
. 53
3.6
The small-world experiment
. 54
3.7
Snowball sampling, contact tracing, and random walks
. 58
4
Networks of information
63
4.1
The World Wide Web
. 63
4.2
Citation networks
. 67
4.3
Other information networks
. 72
5
Biological networks
78
5.1
Biochemical networks
. 78
5.2
Neural networks
. 94
5.3
Ecological networks
. 99
ν
Contents
II Fundamentals of network theory
107
6
Mathematics of networks
109
6.1
Networks and their representation
. 109
6.2
The adjacency matrix
. 110
6.3
Weighted networks
. 112
6.4
Directed networks
. 114
6.5
Hypergraphs
. 122
6.6
Bipartite networks
. 123
6.7
Trees
. 127
6.8
Planar networks
. 129
6.9
Degree
. 133
6.10
Paths
. 136
6.11
Components
. 142
6.12
Independent paths, connectivity, and cut sets
. 145
6.13
The graph Laplacian
. 152
6.14
Random walks
. 157
7
Measures and metrics
168
7.1
Degree centrality
. 168
7.2
Eigenvector centrality
. 169
7.3
Katz centrality
. 172
7.4
PageRank
. 175
7.5
Hubs and authorities
. 178
7.6
Closeness centrality
. 181
7.7
Betweenness centrality
. 185
7.8
Groups of vertices
. 193
7.9
Transitivity
. 198
7.10
Reciprocity
. 204
7.11
Signed edges and structural balance
. 206
7.12
Similarity
. 211
7.13
Homophily and assortative mixing
. 220
8
The large-scale structure of networks
235
8.1
Components
. 235
8.2
Shortest paths and the small-world effect
. 241
8.3
Degree distributions
. 243
8.4
Power laws and scale-free networks
. 247
8.5
Distributions of other centrality measures
. 261
8.6
Clustering coefficients
. 262
vi
Contents
8.7
Assortative
mixing.
266
III
Computer
algorithms
273
9
Basic concepts
of algorithms
275
9.1
Running time and computational complexity
. 278
9.2
Storing network data
. 282
9.3
The adjacency matrix
. 283
9.4
The adjacency list
. 286
9.5
Trees
. 290
9.6
Other network representations
. 298
9.7
Heaps
. 301
10
Fundamental network algorithms
308
10.1
Algorithms for degrees and degree distributions
. 308
10.2
Clustering coefficients
. 310
10.3
Shortest paths and breadth-first search
. 315
10.4
Shortest paths in networks with varying edge lengths
. 329
10.5
Maximum flows and minimum cuts
. 333
11
Matrix algorithms and graph partitioning
345
11.1
Leading eigenvectors and eigenvector
centrality
. 345
11.2
Dividing networks into clusters
. 354
11.3
Graph partitioning
. 358
11.4
The Kernighan-Lin algorithm
. 360
11.5
Spectral partitioning
. 364
11.6
Community detection
. 371
11.7
Simple modularity maximization
. 373
11.8
Spectral modularity maximization
. 375
11.9
Division into more than two groups
. 378
11.10
Other modularity maximization methods
. 380
11.11
Other algorithms for community detection
. 382
IV Network models
395
12
Random graphs
397
12.1
Random graphs
. 398
12.2
Mean number of edges and mean degree
. 400
12.3
Degree distribution
. 401
vu
Contents
12.4
Clustering coefficient
. 402
12.5
Giant component
. 403
12.6
Small components
. 408
12.7
Path lengths
. 419
12.8
Problems with the random graph
. 423
13
Random graphs with general degree distributions
428
13.1
Generating functions
. 429
13.2
The configuration model
. 434
13.3
Excess degree distribution
. 445
13.4
Clustering coefficient
. 449
13.5
Generating functions for degree distributions
. 450
13.6
Number of second neighbors of a vertex
. 451
13.7
Generating functions for the small components
. 456
13.8
Giant component
. 460
13.9
Size distribution for small components
. 465
13.10
Power-law degree distributions
. 470
13.11
Directed random graphs
. 473
14
Models of network formation
486
14.1
Preferential attachment
. 487
14.2
The model of
Barabási
and Albert
. 500
14.3
Further properties of preferential attachment models
. 503
14.4
Extensions of preferential attachment models
. 514
14.5
Vertex copying models
. 534
14.6
Network optimization models
. 541
15
Other network models
552
15.1
The small-world model
. 552
15.2
Exponential random graphs
. 565
V Processes on networks
589
16
Percolation and network resilience
591
16.1
Percolation
. 592
16.2
Uniform random removal of vertices
. 594
16.3
Non-uniform removal of vertices
. 609
16.4
Percolation in real-world networks
. 615
16.5
Computer algorithms for percolation
. 616
vin
Contents
17
Epidemics on
networks
627
17.1
Models of the spread of disease
. 627
17.2
The SI model
. 628
17.3
The SIR model
. 631
17.4
The SIS model
. 636
17.5
The SIRS model
. 637
17.6
Epidemic models on networks
. 639
17.7
Late-time properties of epidemics on networks
. 640
17.8
Late-time properties of the SIR model
. 642
17.9
Time-dependent properties of epidemics on networks
. 648
17.10
Time-dependent properties of the SI model
. 648
17.11
Time-dependent properties of the SIR model
. 661
17.12
Time-dependent properties of the SIS model
. 669
18
Dynamical systems on networks
676
18.1
Dynamical systems
. 677
18.2
Dynamics on networks
. 686
18.3
Dynamics with more than one variable per vertex
. 695
18.4
Synchronization
. 701
19
Network search
705
19.1
Web search
. 705
19.2
Searching distributed databases
. 709
19.3
Message passing
. 713
References
727
Index
740
IX |
| any_adam_object | 1 |
| author | Newman, Mark E. J. |
| author_GND | (DE-588)133013073 |
| author_facet | Newman, Mark E. J. |
| author_role | aut |
| author_sort | Newman, Mark E. J. |
| author_variant | m e j n mej mejn |
| building | Verbundindex |
| bvnumber | BV037182173 |
| classification_rvk | QP 345 SK 890 ST 200 |
| classification_tum | DAT 250f MAT 904f |
| ctrlnum | (OCoLC)723424002 (DE-599)BVBBV037182173 |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | Reprinted three times |
| format | Book |
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| id | DE-604.BV037182173 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:28:01Z |
| institution | BVB |
| isbn | 9780199206650 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021096762 |
| oclc_num | 723424002 |
| open_access_boolean | |
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| physical | XI, 772 S., IV Taf. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spellingShingle | Newman, Mark E. J. Networks an introduction Computer networks Social networks Computer networks / Mathematics Social networks / Mathematics Mathematik Soziales Netzwerk (DE-588)4055762-5 gnd Rechnernetz (DE-588)4070085-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Netzwerk (DE-588)4171529-9 gnd Netzwerktheorie (DE-588)4171531-7 gnd |
| subject_GND | (DE-588)4055762-5 (DE-588)4070085-9 (DE-588)4114528-8 (DE-588)4171529-9 (DE-588)4171531-7 |
| title | Networks an introduction |
| title_auth | Networks an introduction |
| title_exact_search | Networks an introduction |
| title_full | Networks an introduction M. E. J. Newman |
| title_fullStr | Networks an introduction M. E. J. Newman |
| title_full_unstemmed | Networks an introduction M. E. J. Newman |
| title_short | Networks |
| title_sort | networks an introduction |
| title_sub | an introduction |
| topic | Computer networks Social networks Computer networks / Mathematics Social networks / Mathematics Mathematik Soziales Netzwerk (DE-588)4055762-5 gnd Rechnernetz (DE-588)4070085-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Netzwerk (DE-588)4171529-9 gnd Netzwerktheorie (DE-588)4171531-7 gnd |
| topic_facet | Computer networks Social networks Computer networks / Mathematics Social networks / Mathematics Mathematik Soziales Netzwerk Rechnernetz Mathematisches Modell Netzwerk Netzwerktheorie |
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