A first course in network theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2015
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 254 S. Ill., graph. Darst. |
| ISBN: | 9780198726463 0198726465 9780198726456 |
Internformat
MARC
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| 100 | 1 | |a Estrada, Ernesto |d 1966- |e Verfasser |0 (DE-588)1018297634 |4 aut | |
| 245 | 1 | 0 | |a A first course in network theory |c Ernesto Estrada ; Philip A. Knight |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2015 | |
| 300 | |a XIV, 254 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Netzwerktheorie |0 (DE-588)4171531-7 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Knight, Philip A. |e Verfasser |0 (DE-588)1069643718 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027683275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804152787879067648 |
|---|---|
| adam_text | Contents
1
Introduction
to Network Theory
1
1.1
Overview of networks
1
1.2
History of graphs
5
1.3
What you will learn from this book
9
Further reading
11
2
General Concepts in Network Theory
12
2.1
Formal definition of networks
12
13
16
21
26
30
31
31
32
34
35
36
37
38
38
4
Data Analysis and Manipulation
39
4.1
Motivation
39
4.2
Sources of error
40
4.3
Processing data
42
4.4
Data statistics and random variables
46
4.5
Experimental tools
48
Further reading
51
5
Algebraic Concepts in Network Theory
52
5.1
Basic definitions of networks and matrices
52
52
Eigenvalues and eigenvectors
54
Further reading
65
2.2
Elementary graph theory concepts
2.3
Networks and matrices
2.4
Network connectivity
2.5
Graph structures
Further reading
How
To Prove It
3.1
Motivation
3.2
Draw pictures
3.3
Use induction
3.4
Try to find a counterexample
3.5
Proof by contradiction
3.6
Make connections between concepts
3.7
Other general advice
Further reading
xii
Contenu
6
Spectra
of Adjacency Matrices
6.1
Motivation
„
6.2
Spectral analysis of simple networks
6.3
Spectra and structure
6.4
Eigenvectors of the adjacency matrix
Further reading
78
7
The Network Laplacian
78
7.1
The graph Laplacian
7.2
Eigenvalues and eigenvectors of the graph Laplacian ^
Further reading
8
Classical Physics Analogies
tó
8.1
Motivation w
8.2
Classical mechanical analogies °
8.3
Networks as electrical circuits
Further reading
9
Degree
Distribution·
95
9.1
Motivation 95
9.2
General degree distributions
5
9.3
Scale-free networks 97
Further reading 10°
10
Chmermg Coefficients of Networks
101
10.1
Motivation
101
10.2
The Wins-Strogatz
dustering
coefficient I01
10.3
The Newman clustering coefficient
102
Further reading
104
И
Random
Modebof
Networks 10S
111 Motivation
105
IU The
Erdöfr-Rényi
model of random networks
105
11-3
The Barabtst-Alben model
108
114
TtttWms-Strogatzmodd
110
Further reading
цЗ
U
Matrix Functions
ц4
111 Mothwion
П4
Ш
Matrix
powert
ц4
12J
Tne
matrix exponential
П8
MA Bxiendng matrix powers 12i
115 General manttftmcoom
12з
rVatereadta« l28
Contents
xiii
13
Fragment-based Measures
129
13.1
Motivation
129
13.2
Counting subgraphs in networks
129
13.3
Network motifs
140
Further reading
142
14
Classical Node Centrality
143
14.1
Motivation
143
14.2
Degree centrality
143
14.3
Closeness centrality
146
14.4
Betweenness centrality
152
Further reading
156
15
Spectral Node Centrality
157
15.1
Motivation
157
15.2
Katz centrality
158
15.3
Eigenvector centrality
160
15.4
Subgraph centrality
164
Further reading
169
16
Quantum Physics Analogies
170
16.1
Motivation
170
16.2
Quantum mechanical analogies
171
16.3
Tight-binding models
174
16.4
Some specific quantum-mechanical systems
177
Further reading
178
17
Global Properties of Networks I
179
. 1
Motivation
1
79
.2
Degree-degree correlation
179
3
Network reciprocity
187
.4
Network returnability
189
Further reading
191
18
Global Properties of Networks
Π
192
18.1
Motivation
192
18.2
Network expansion properties
192
18.3
Spectral scaling method
195
18.4
Bipartiviry measures
200
Further reading
205
19
Communicability in Networks
206
19.1
Motivation
206
19.2
Network communicabilitv
207
xiv
Стили
19.3
Communicability distance
212
Further reading
216
20
Statistical Physics Analogies
217
20.1
Motivation
217
20.2
Thermodynamics in a nutshell
218
20.3
Micro-canonical ensembles
220
20.4
The canonical ensemble
221
20.5
The temperature in network theory
225
Further reading
226
2!
Communi
tie· in
Networks
227
21.1
Motivation
227
21.2
Basic concepts of communities
229
21.3
Network partition methods
230
21.4
Clustering by centrality
235
21.5
Modularity
237
2
1
.6
Communities based on communicability
239
21.7
Anti-communities
245
Further reading
250
Index
251
|
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| discipline | Informatik Elektrotechnik Mathematik |
| edition | 1. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:16:16Z |
| institution | BVB |
| isbn | 9780198726463 0198726465 9780198726456 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027683275 |
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| spelling | Estrada, Ernesto 1966- Verfasser (DE-588)1018297634 aut A first course in network theory Ernesto Estrada ; Philip A. Knight 1. ed. Oxford Oxford Univ. Press 2015 XIV, 254 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 s DE-604 Knight, Philip A. Verfasser (DE-588)1069643718 aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027683275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Estrada, Ernesto 1966- Knight, Philip A. A first course in network theory Netzwerktheorie (DE-588)4171531-7 gnd |
| subject_GND | (DE-588)4171531-7 |
| title | A first course in network theory |
| title_auth | A first course in network theory |
| title_exact_search | A first course in network theory |
| title_full | A first course in network theory Ernesto Estrada ; Philip A. Knight |
| title_fullStr | A first course in network theory Ernesto Estrada ; Philip A. Knight |
| title_full_unstemmed | A first course in network theory Ernesto Estrada ; Philip A. Knight |
| title_short | A first course in network theory |
| title_sort | a first course in network theory |
| topic | Netzwerktheorie (DE-588)4171531-7 gnd |
| topic_facet | Netzwerktheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027683275&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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