Graph spectra for complex networks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2012
|
| Ausgabe: | 1. publ., 1. paperback ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally published: 2011 |
| Beschreibung: | XI, 346 S. Ill. |
| ISBN: | 9781107411470 1107411475 9780521194587 |
Internformat
MARC
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| 020 | |a 9781107411470 |c Paperback |9 978-1-107-41147-0 | ||
| 020 | |a 1107411475 |9 1-107-41147-5 | ||
| 020 | |a 9780521194587 |c Hardback |9 978-0-521-19458-7 | ||
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| 100 | 1 | |a Mieghem, Piet van |d 1964- |e Verfasser |0 (DE-588)131444018 |4 aut | |
| 245 | 1 | 0 | |a Graph spectra for complex networks |c Piet Van Mieghem |
| 250 | |a 1. publ., 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2012 | |
| 300 | |a XI, 346 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Originally published: 2011 | ||
| 650 | 4 | |a Graph theory | |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 1 | |a Komplexes System |0 (DE-588)4114261-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025218285&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025218285 | ||
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Datensatz im Suchindex
| _version_ | 1804149408973979648 |
|---|---|
| adam_text | Contents
Preface
ix
Acknowledgements xiii
Symbols xv
1
Introduction
1
1.1 Interpretation and
contemplation
2
1.2 Outline
of the book
5
1.3
Classes of graphs
7
1.4
Outlook
10
Parti Spectra of graphs
11
2
Algebraic graph theory
13
2.1
Graph related matrices
13
2.2
Walks and paths
25
3
Eigenvalues of the adjacency matrix
29
3.1
General properties
29
3.2
The number of walks
33
3.3
Regular graphs
43
3.4
Bounds for the largest, positive eigenvalue
λι
46
3.5
Eigenvalue spacings
55
3.6
Additional properties
58
3.7
The stochastic matrix
Ρ
=
Δ 1
A
63
4
Eigenvalues of the Laplacian
Q
67
4.1
General properties
67
vi
Contents
4.2
Second
smallest eigenvalue of the Laplacian
Q
80
4.3
Partitioning of a graph
89
4.4
The modularity and the modularity matrix
M
96
4.5
Bounds for the diameter
108
4.6
Eigenvalues of graphs and subgraphs
109
5
Spectra of special types of graphs
115
5.1
The complete graph
115
5.2
A small-world graph
115
5.3
A circuit on
N
nodes
123
5.4
A path of
N - 1
hops
124
5.5
A path of
h
hops
129
5.6
The wheel Wn+i
129
5.7
The complete bipartite graph Km,n
129
5.8
A general bipartite graph
131
5.9
Complete multi-partite graph
135
5.10
An m-fully meshed star topology
138
5.11
A chain of cliques
147
5.12
The lattice
154
6
Density function of the eigenvalues
159
6.1
Definitions
159
6.2
The density when
N —>
oo
161
6.3
Examples of spectral density functions
163
6.4
Density of a sparse regular graph
166
6.5
Random matrix theory
169
7
Spectra of complex networks
179
7.1
Simple observations
179
7.2
Distribution of the Laplacian eigenvalues and of the degree
181
7.3
Functional brain network
184
7.4
Rewiring Watts-Strogatz small-world graphs
185
7.5
Assortati
vity
187
7.6
Reconstructability of complex networks
196
7.7
Reaching consensus
199
7.8
Spectral graph metrics
200
Part II
Eigensystem
and polynomials
209
8 Eigensystem
of a matrix
211
8.1
Eigenvalues and eigenvectors
211
8.2
Functions of a matrix
219
Contents
vii
8.3
Hermitian and real symmetric matrices
222
8.4
Vector and matrix norms
230
8.5
Non-negative matrices
235
8.6
Positive (semi) defmiteness
240
8.7
Interlacing
243
8.8
Eigenstructure of the product
AB
252
8.9
Formulae of determinants
255
9
Polynomials with real coefficients
263
9.1
General properties
263
9.2
Transforming polynomials
270
9.3
Interpolation
274
9.4
The Euclidean algorithm
277
9.5
Descartes rule of signs
282
9.6
The number of real zeros in an interval
292
9.7
Locations of zeros in the complex plane
295
9.8
Zeros of complex functions
302
9.9
Bounds on values of a polynomial
305
9.10
Bounds for the spacing between zeros
306
9.11
Bounds on the zeros of a polynomial
308
10
Orthogonal polynomials
313
10.1
Definitions
313
10.2
Properties
315
10.3
The three-term recursion
317
10.4
Zeros of orthogonal polynomials
323
10.5
Gaussian quadrature
326
10.6
The Jacobi matrix
331
References
339
Index
345
|
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| dewey-full | 511.5 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ., 1. paperback ed. |
| format | Book |
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| id | DE-604.BV040364529 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:22:32Z |
| institution | BVB |
| isbn | 9781107411470 1107411475 9780521194587 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025218285 |
| oclc_num | 798409287 |
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| owner | DE-19 DE-BY-UBM DE-11 DE-739 DE-1050 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-739 DE-1050 |
| physical | XI, 346 S. Ill. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Mieghem, Piet van 1964- Verfasser (DE-588)131444018 aut Graph spectra for complex networks Piet Van Mieghem 1. publ., 1. paperback ed. Cambridge [u.a.] Cambridge University Press 2012 XI, 346 S. Ill. txt rdacontent n rdamedia nc rdacarrier Originally published: 2011 Graph theory Komplexes System (DE-588)4114261-5 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Komplexes System (DE-588)4114261-5 s 1\p DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025218285&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mieghem, Piet van 1964- Graph spectra for complex networks Graph theory Komplexes System (DE-588)4114261-5 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4113782-6 |
| title | Graph spectra for complex networks |
| title_auth | Graph spectra for complex networks |
| title_exact_search | Graph spectra for complex networks |
| title_full | Graph spectra for complex networks Piet Van Mieghem |
| title_fullStr | Graph spectra for complex networks Piet Van Mieghem |
| title_full_unstemmed | Graph spectra for complex networks Piet Van Mieghem |
| title_short | Graph spectra for complex networks |
| title_sort | graph spectra for complex networks |
| topic | Graph theory Komplexes System (DE-588)4114261-5 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graph theory Komplexes System Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025218285&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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