Graph theory and complex networks: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[S.l.]
Maarten van Steen
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references (p.279-285) and index |
| Beschreibung: | XII, 285 S. Ill., graph. Darst. 23 cm |
| ISBN: | 9789081540612 9081540610 |
Internformat
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| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Graph theory / Data processing | |
| 650 | 4 | |a System analysis | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
1 Introduction 1
1.1 Communication networks..................................... 4
Historical perspective..................................... 4
From telephony to the Internet............................. 6
The Web and Wikis.......................................... 8
1.2 Social networks.......................................... 9
Online communities ........................................ 9
Traditional social networks .............................. 10
1.3 Networks everywhere....................................... 11
1.4 Organization of this book................................. 13
2 Foundations 17
2.1 Formalities............................................... 18
Graphs and vertex degrees................................. 18
Degree sequence........................................... 23
Subgraphs and line graphs................................. 28
2.2 Graph representations..................................... 31
Data structures .......................................... 31
Graph isomorphism ........................................ 33
2.3 Connectivity.............................................. 37
2.4 Drawing graphs............................................ 45
Graph embeddings.......................................... 45
Planar graphs............................................. 50
3 Extensions 55
3.1 Directed graphs.......................................... 57
Basics of directed graphs................................. 57
v
vi CONTENTS
Connectivity for directed graphs........................... 61
3.2 Weighted graphs ........................................... 65
3.3 Colorings.................................................. 69
Edge colorings............................................. 69
Vertex colorings........................................... 71
4 Network traversal 79
4.1 Euler tours................................................ 81
Constructing an Euler tour................................. 82
The Chinese postman problem................................ 87
4.2 Hamilton cycles............................................ 92
Properties of Hamiltonian graphs........................... 92
Finding a Hamilton cycle................................... 97
Optimal Hamilton cycles....................................100
5 Trees 105
5.1 Background.................................................107
Trees in transportation networks...........................107
Trees as data structures...................................109
5.2 Fundamentals...............................................112
5.3 Spanning trees.............................................116
5.4 Routing in communication networks..........................119
Dijkstra s algorithm.......................................120
The Bellman-Ford algorithm.................................123
A note on algorithmic performance..........................127
6 Network analysis 131
6.1 Vertex degrees.............................................133
Degree distribution........................................134
Degree correlations...................................... 136
6.2 Distance statistics........................................140
6.3 Clustering coefficient.....................................143
Some effects of clustering ................................143
Local view............................................... 144
Global view................................................146
6.4 Centrality .............................................. 150
7 Random networks 155
7.1 Introduction...............................................157
7.2 Classical random networks .................................158
Degree distribution........................................159
Other metrics for random graphs............................162
CONTENTS
vii
7.3 Small worlds..............................................167
7A Scale-free networks.......................................172
Fundamentals..............................................173
Properties of scale-free networks.........................178
Related networks..........................................182
8 Modern computer networks 185
8.1 The Internet..............................................187
Computer networks.........................................187
Measuring the topology of the Internet....................192
8.2 Peer-to-peer overlay networks.............................195
Structured overlay networks...............................196
Random overlay networks...................................204
8.3 The World Wide Web...................................... 212
The organization of the Web............................. 212
Measuring the topology of the Web.........................214
9 Social networks 223
9.1 Social network analysis: introduction ....................225
Examples..................................................225
Historical background.....................................227
Sociograms in practice: a teacher s aid...................231
9.2 Some basic concepts ......................................234
Centrality and prestige...................................234
Structural balance........................................240
Cohesive subgroups .......................................246
Affiliation networks......................................252
9.3 Equivalence...............................................254
Structural equivalence....................................255
Automorphic equivalence...................................258
Regular equivalence ......................................259
Conclusions 261
Mathematical notations 267
Index 271
Bibliography 279
Graph Theory and Complex Networks aims to explain the basics of graph theory that are
needed at an introductory level for students in computer or information sciences. To
motivate students and to show that even these basic notions can be extremely useful, the
book also aims to provide an introduction to the modern field of network science.
Mathematics is often unnecessarily difficult for students, at times even intimidating. For this
reason, explicit attention is paid in the first chapters to mathematical notations and proof
techniques, emphasizing that the notations form the biggest obstacle, not the mathematical
concepts themselves. This approach allows to gradually prepare students for using tools
that are necessary to put graph theory to work; complex networks.
In the second part of the book the student learns about random networks, small worlds, the
structure of the Internet and the Web, peer-to-peer systems, and social networks. Again,
everything is discussed at an elementary level, but such that in the end students indeed
have the feeling that they:
1. Have learned how to read and understand the basic mathematics related to graph
theory.
2. Understand how basic graph theory can be applied to optimization problems such
as routing in communication networks.
3. Know a bit more about this sometimes mystical field of small worlds and random
networks.
There is an accompanying web site www.distributed-systems.net/gtcn from where
supplementary material can be obtained, including exercises, Mathematica notebooks, data
for analyzing graphs, and generators for various complex networks.
|
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| language | English |
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| spelling | Steen, Maarten van Verfasser (DE-588)124643426 aut Graph theory and complex networks an introduction Maarten van Steen [S.l.] Maarten van Steen 2010 XII, 285 S. Ill., graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p.279-285) and index Graph theory Graph theory / Data processing System analysis Datenverarbeitung Graphentheorie (DE-588)4113782-6 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Netzwerktheorie (DE-588)4171531-7 s 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=025218265&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=025218265&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Steen, Maarten van Graph theory and complex networks an introduction Graph theory Graph theory / Data processing System analysis Datenverarbeitung Graphentheorie (DE-588)4113782-6 gnd Netzwerktheorie (DE-588)4171531-7 gnd |
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| title | Graph theory and complex networks an introduction |
| title_auth | Graph theory and complex networks an introduction |
| title_exact_search | Graph theory and complex networks an introduction |
| title_full | Graph theory and complex networks an introduction Maarten van Steen |
| title_fullStr | Graph theory and complex networks an introduction Maarten van Steen |
| title_full_unstemmed | Graph theory and complex networks an introduction Maarten van Steen |
| title_short | Graph theory and complex networks |
| title_sort | graph theory and complex networks an introduction |
| title_sub | an introduction |
| topic | Graph theory Graph theory / Data processing System analysis Datenverarbeitung Graphentheorie (DE-588)4113782-6 gnd Netzwerktheorie (DE-588)4171531-7 gnd |
| topic_facet | Graph theory Graph theory / Data processing System analysis Datenverarbeitung Graphentheorie Netzwerktheorie |
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