Structure in Complex Networks:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Edition: | 1. ed. |
| Series: | Lecture Notes in Physics
766 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 151 S. graph. Darst. |
| ISBN: | 9783540878322 |
Staff View
MARC
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| 245 | 1 | 0 | |a Structure in Complex Networks |c J. Reichardt |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 151 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Data mining | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Pattern recognition systems | |
| 650 | 4 | |a Statistical physics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction
to Complex Networks
........................ 1
1.1
Graph Theoretical Notation
.............................. 2
1.2
Random Graphs
......................................... 3
1.3
Six Degrees of Separation
................................. 4
1.4
Scale-Free Degree Distributions
........................... 5
1.5
Correlations in Networks
................................. 6
1.6
Dynamics on Networks
................................... 7
1.7
Patterns of Link Structure
................................ 8
References
.................................................. 10
Standard Approaches to Network Structure: Block
Modeling
.................................................. 13
2.1
Positions, Roles and Equivalences
......................... 13
2.2
Block Modeling
......................................... 14
2.3
Cohesive Subgroups or Communities as Block Models
........ 18
2.3.1
Sociological Definitions
............................. 18
2.3.2
Definitions from Physicists
......................... 20
2.4
Algorithms for Community Detection
...................... 21
2.4.1
Comparing a Quality Function
...................... 21
2.4.2
Hierarchical Algorithms
............................ 22
2.4.3
Semi-hierarchical
.................................. 25
2.4.4
Non-hierarchical
................................... 25
2.4.5
Optimization Based
............................... 26
2.5
Conclusion
............................................. 27
References
.................................................. 27
A First Principles Approach to Block Structure Detection
. 31
3.1
Mapping the Problem
.................................... 31
3.1.1
Dimensionality Reduction with Minimal Squared Error
. 31
XII Contents
3.1.2
Squared Error for Multivariate Data and Networks
.... 33
3.2
A New Error Function
................................... 34
3.2.1
Fitting Networks to Image Graphs
................... 37
3.2.2
The Optimal Image Graph
......................... 37
3.2.3
Maximum Value of the Fit Score
.................... 38
3.2.4
Choice of a Penalty Function and Null Model
......... 39
3.2.5
Cohesion and Adhesion
............................ 40
3.2.6
Optimizing the Quality Function
.................... 40
3.3
Conclusion
............................................. 42
References
.................................................. 43
4
Diagonal Block Models as Cohesive Groups
............... 45
4.1
Equivalence with Newman-Girvan Modularity and Spin
Glass Energy
........................................... 45
4.1.1
Properties of the Ground State
...................... 46
4.1.2
Simple Divisive and Agglomerative Approaches
to Modularity Maximization
........................ 48
4.1.3
Finding the Community Around a Given Node
........ 51
4.2
Comparison with Other Definitions of Communities
.......... 51
4.2.1
Hierarchy and Overlap of Community Assignments
.... 52
4.3
Benchmarking the Algorithm
............................. 56
4.4
Community Detection and Graph Partitioning
.............. 60
4.4.1
Expectation Values for the Modularity
............... 61
4.4.2
Theoretical Limits of Community Detection
.......... 66
4.5
Conclusion
............................................. 67
References
.................................................. 67
5
Modularity of Dense Random Graphs
..................... 69
5.1
Analytical Developments
................................. 69
5.2
Numerical Experiments
.................................. 80
References
.................................................. 85
6
Modularity of Sparse Random Graphs
..................... 87
6.1
Graph Partitioning Using the Cavity Method
............... 87
6.1.1
Cavity Method at Zero Temperature
................. 88
6.1.2
Symmetry Conditions
.............................. 91
6.1.3
Bi-partitioning
.................................... 92
6.1.4
Limit of Dense Graphs with Poissonian Degree
Distribution
...................................... 97
6.1.5
q-Partitioning of a Bethe Lattice with three Links per
Node
............................................ 98
6.1.6
Population Dynamics Approximation
................101
6.2
Recovering Planted Cluster Structures
.....................102
6.2.1
Symmetry Conditions
..............................104
6.2.2
Graphs with Two Clusters
..........................106
Contents XIII
6.2.3
Onset of Detectable Cluster Structure
................109
6.2.4
Graphs with More than Two Clusters
................
Ill
6.2.5
Bethe Lattice with
к
= 3...........................112
6.2.6
Population Dynamics Formulation of the Cavity
Equations
........................................112
6.3
Conclusion
.............................................115
References
..................................................117
7
Applications
...............................................119
7.1
Block Modeling the World Trade Network
..................119
7.2
Communities of Common Interest among eBay Users
........126
7.2.1
Data Set
.........................................129
7.2.2
User Activity
.....................................130
7.2.3
User Networks
....................................132
7.2.4
Market Segmentation
..............................136
7.3
Summary
...............................................144
References
..................................................145
8
Conclusion and Outlook
...................................149
|
| any_adam_object | 1 |
| author | Reichardt, Jörg |
| author_GND | (DE-588)133779262 |
| author_facet | Reichardt, Jörg |
| author_role | aut |
| author_sort | Reichardt, Jörg |
| author_variant | j r jr |
| building | Verbundindex |
| bvnumber | BV035218616 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)248993741 (DE-599)DNB990121623 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
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| discipline | Physik Informatik Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV035218616 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:28:52Z |
| institution | BVB |
| isbn | 9783540878322 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017024724 |
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| physical | XIII, 151 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Physics |
| series2 | Lecture Notes in Physics |
| spelling | Reichardt, Jörg Verfasser (DE-588)133779262 aut Structure in Complex Networks J. Reichardt 1. ed. Berlin [u.a.] Springer 2009 XIII, 151 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Physics 766 Komplexes System - Netzwerk <Graphentheorie> - Zufallsgraph - Blockmodellanalyse - Spinmodell Cluster analysis Data mining Graph theory Pattern recognition systems Statistical physics Blockmodellanalyse (DE-588)4694481-3 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 gnd rswk-swf Spinmodell (DE-588)4272227-5 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Netzwerk Graphentheorie (DE-588)4705155-3 gnd rswk-swf Komplexes System (DE-588)4114261-5 s Netzwerk Graphentheorie (DE-588)4705155-3 s Zufallsgraph (DE-588)4277661-2 s Blockmodellanalyse (DE-588)4694481-3 s Spinmodell (DE-588)4272227-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-87833-9 Lecture Notes in Physics 766 (DE-604)BV000003166 766 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017024724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reichardt, Jörg Structure in Complex Networks Lecture Notes in Physics Komplexes System - Netzwerk <Graphentheorie> - Zufallsgraph - Blockmodellanalyse - Spinmodell Cluster analysis Data mining Graph theory Pattern recognition systems Statistical physics Blockmodellanalyse (DE-588)4694481-3 gnd Zufallsgraph (DE-588)4277661-2 gnd Spinmodell (DE-588)4272227-5 gnd Komplexes System (DE-588)4114261-5 gnd Netzwerk Graphentheorie (DE-588)4705155-3 gnd |
| subject_GND | (DE-588)4694481-3 (DE-588)4277661-2 (DE-588)4272227-5 (DE-588)4114261-5 (DE-588)4705155-3 |
| title | Structure in Complex Networks |
| title_auth | Structure in Complex Networks |
| title_exact_search | Structure in Complex Networks |
| title_full | Structure in Complex Networks J. Reichardt |
| title_fullStr | Structure in Complex Networks J. Reichardt |
| title_full_unstemmed | Structure in Complex Networks J. Reichardt |
| title_short | Structure in Complex Networks |
| title_sort | structure in complex networks |
| topic | Komplexes System - Netzwerk <Graphentheorie> - Zufallsgraph - Blockmodellanalyse - Spinmodell Cluster analysis Data mining Graph theory Pattern recognition systems Statistical physics Blockmodellanalyse (DE-588)4694481-3 gnd Zufallsgraph (DE-588)4277661-2 gnd Spinmodell (DE-588)4272227-5 gnd Komplexes System (DE-588)4114261-5 gnd Netzwerk Graphentheorie (DE-588)4705155-3 gnd |
| topic_facet | Komplexes System - Netzwerk <Graphentheorie> - Zufallsgraph - Blockmodellanalyse - Spinmodell Cluster analysis Data mining Graph theory Pattern recognition systems Statistical physics Blockmodellanalyse Zufallsgraph Spinmodell Komplexes System Netzwerk Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017024724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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