Analysis of complex networks: from biology to linguistics
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Weinheim
WILEY-VCH
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVIII, 462 S. Ill., graph. Darst. |
| ISBN: | 9783527323456 |
Internformat
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| 300 | |a XVIII, 462 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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Titel: Analysis of complex networks
Autor: Dehmer, Matthias
Jahr: 2009
I V
Contents
Preface XIII
List of Contributors XV
1 Entropy, Orbits, and Spectra of Craphs 7
Abbe Mowshowitz and Valia Mitsou
1-1 Introduction 1
1.2 Entropy orthe Information Content ofGraphs 2
1.3 Groups and Graph Spectra 4
1.4 Approximating Orbits 11
1.4.1 The Degree of the Vertices 13
1-4.2 The Point-Deleted Neighborhood Degree Vector 13
1-4.3 Betweenness Centrality 15
1-5 Alternative Bases for Structural Complexity 19
References 21
2 Statistical Mechanics of Complex Networks 23
Stefan Thurner
2-1 Introduction 23
2.1.1 Network Entropies 25
2.1.2 Network Hamiltonians 27
2.1.3 Network Ensembles 28
2.1.4 Some Definitions of Network Measures 30
2.2 Macroscopics: Entropies for Networks 31
2.2.1 A General Set of Network Models Maximizing Generalized
Entropies 32
2.2.1.1 A Unified Network Model 32
2.2.1.2 Famous Limits of the Unified Model 35
2.2.1.3 Unified Model: Addirional Features 35
2-3 Microscopics: Hamiltonians of Networks - Network
Thermodynamics 35
VI I Contents
2.3.1 Topological Phase Transitions 36
2.3.2 A Note on Entropy 37
2.4 Ensembles of Random Networks - Superstatistics 39
2.5 Conclusion 42
References 43
3 A Simple Integrated Approach to Network Complexity and
Node Centrality 47
Danail Bonchev
3.1 Introduction 47
3.2 The Small-World Connectivity Descnptors 49
3.3 The Integrated Centrality Measure 52
References 53
4 Spectral Theory of Networks:
Prom Biomolecular to Ecological Systems 55
Ernesto Estrada
4.1 Introduction 55
4.2 Background on Graph Spectra 56
4.3 Spectral Measures of Node Centrality 58
4.3.1 Subgraph Centrality as a Partition Function 60
4.3.2 Application 61
4.4 Global Topological Organization of Complex Networks 62
4.4.1 Spectral Scaling Method 63
4.4.2 Universal Topological Classes of Networks 65
4.4.3 Applications 68
4.5 Communicability in Complex Networks 69
4.5.1 Communicability and Network Communities 71
4.5.2 Detection of Communities: The Communicability Graph 73
4.5.3 Application 74
4.6 Network Bipartivity 76
4.6.1 Detecting Bipartite Substructures in Complex Networks 77
4.6.2 Application 80
4.7 Conclusion 80
References 81
5 On the Structure of Neutral Networks of RNA Pseudoknot
Structures 85
Christian M. Reidys
5.1 Motivation and Background 85
5.1.1 Notation and Terminology 87
5.2 Preliminaries 88
5.3 Connectivity 90
Contents I VII
5.4 The Largest Component 93
5.5 Distances in n-Cubes 105
5.6 Conclusion 110
References 111
6 Graph Edit Distance - Optimal and Suboptimal Algorithms
with Applications 1)3
Horst Bunke and Kaspar Riesen
6.1 Introduction 113
6.2 Graph Edit Distance 115
6.3 Computation of GED 118
6.3.1 Optimal Algorithms 118
6.3.2 Suboptimal Algorithms 121
6.3.2.1 Bipartite Graph Matching 121
6.4 Applications 125
6.4.1 Graph Data Sets 125
6.4.2 GED-Based Nearest-Neighbor Classification 129
6.4.3 Dissimilarity-Based Embedding Graph Kernels 129
6.5 Experimental Evaluation 132
6.5.1 Optimal vs. Suboptimal Graph Edit Distance 133
6.5.2 Dissimilarity Embedding Graph Kernels
Based on Suboptimal Graph Edit Distance 236
6.6 Summary and Conclusions 139
References 140
7 Graph Energy 745
Ivan Cutman, Xueliang Li, andjianbin Zhang
7.1 Introduction 145
7.2 Bounds forthe Energy ofGraphs 147
7.2.1 Some Upper Bounds 147
7.2.2 Some Lower Bounds 154
7.3 Hyperenergetic, Hypoenergetic, and Equienergetic Graphs 156
7.3.1 Hyperenergetic Graphs 156
7.3.2 Hypoenergetic Graphs 157
7.3.3 Equienergetic Graphs 257
7.4 Graphs Extremal with Regard to Energy 262
7.5 Miscellaneous 268
7.6 Concluding Remarks 269
References 170
VIII I Contents
8 Generalized Shortest Path Trees: A Novel Graph Class by Example
ofSemiotic Networks 7 75
Alexander Mehler
8.1 Introduction 175
8.2 A Class ofTree-Like Graphs and Some oflts Derivatives 178
8.2.1 Preliminary Notions 178
8.2.2 Generalized Trees 180
8.2.3 Minimum Spanning Generalized Trees 186
8.2.4 Generalized Shortest Path Trees 190
8.2.5 Shortest Paths Generalized Trees 193
8.2.6 Generalized Shortest Paths Trees 295
8.2.7 Accounting for Orientation: Directed Generalized Trees 198
8.2.8 Generalized Trees, Quality Dimensions,
and Conceptual Domains 204
8.2.9 Generalized Forests as Multidomain Conceptual Spaces 208
8.3 Semiotic Systems as Conceptual Graphs 212
References 218
9 Applications of Graph Theory in Chemo- and Bioinformatics 227
Dimitris Dimitropoulos, Adel Colovin, M.John, and Eugene Krissinel
9.1 Introduction 227.
9.2 Molecular Graphs 222
9.3 Common Problems with Molecular Graphs 223
9.4 ComparisonS and 3D Alignment of Protein Structures 225
9.5 Identification of Macromolecular Assemblies
in Crystal Packing 229
9.6 Chemical Graph Formats 231
9.7 Chemical Software Packages 232
9.8 Chemical Databases and Resources 232
9.9 Subgraph Isomorphism Solution in SQL 232
9.10 Cycles in Graphs 235
9.11 Aromatic Properties 236
9.12 Planar Subgraphs 237
9.13 Conclusion 238
References 239
10 Structural and Functional Dynamics in Cortical and Neuronal
Networks 245
Marcus Kaiser and Jennifer Simonotto
10.1 Introduction 245
10.1.1 Properties of Cortical and Neuronal Networks 246
10.1.1.1 Modularity 247
10.1.1.2 Small-World Features 247
Contents I IX
10.1.1.3 Scale-Free Features 248
10.1.1.4 Spatial Layout 250
10.1.2 Prediction of Neural Connectivity 252
10.1.3 Activity Spreading 254
10.2 Structural Dynamics 255
10.2.1 Robustness Toward Structural Damage 255
10.2.1.1 Removalof Edges 256
10.2.1.2 Removal of Nodes 257
10.2.2 Network Changes During Development 258
10.2.2.1 Spatial Growth Can Generate S mall-World Networks 258
10.2.2.2 Time Windows Generate Multiple Clusters 259
10.3 Functional Dynamics 260
10.3.1 Spreading in Excitable Media 260
10.3.1.1 Cardiac Defibrillarion as a Case Study 261
10.3.1.2 Critical Timing for Changing the State ofthe Cardiac System 261
10.3.2 Topological Inhibition Limits Spreading 262
10.4 Summary 264
References 266
11 Network Mapping of Metabolie Pathways 277
Qiong Cheng and Alexander Zelikovsky
11.1 Introduction 271
11.2 Brief Overview of Network Mapping Methods 273
11.3 Modeling Metabolie Pathway Mappings 275
11.3.1 Problem Formulation 277
11-4 Computing Minimum Cost Homomorphisms 277
11.4.1 The Dynamic Programming Algorithm
for Multi-Source Tree Patterns 278
11.4.2 Handling Cycles in Patterns 280
11.4.3 Allowing Pattern Vertex Deletion 281
11.5 Mapping Metabolie Pathways 282
11.6 Implications of Pathway Mappings 285
11.7 Conclusion 291
References 291
12 Graph Structure Analysis and Computational Tractability
of Scheduling Problems 295
Sergey Sevastyanov and Alexander Kononov
12.1 Introduction 295
12.2 The Connected List Coloring Problem 296
12.3 Some Practical Problems Reducible to the CLC Problem 298
12.3.1 The Problem of Connected Service Areas 298
12.3.2 No-Idle Scheduling on Parallel Machines 300
X Contents
12.3.3 Scheduling ofUnit Jobs on a p-Batch Machine 301
12.4 A Parameterized Class of Subproblems of the CLC Problem 302
12.5 Complexities ofEight Representatives of Class CLC(X) 304
12.5.1 Three NP-Complete Subproblems 304
12.5.2 Five Polynomial-Time Solvable Subproblems 305
12.6 A Basis System of Problems 317
12.7 Conclusion 320
References 322
13 Complexity of Phylogenetic Networks:
Counting Cubes in Mediän Craphs and Related Problems 323
Matjai Kovse
13.1 Introduction 323
13.2 Preliminaries 324
13.2.1 Mediän Graphs 325
13.2.1.1 Expansion Procedure 328
13.2.1.2 The Canonical Metric Representation
and Isometric Dimension 328
13.3 Treelike Equalities and Euler-Type Inequalities 330
13.3.1 Treelike Eequalities and Euler-Type Inequalities
for Mediän Graphs 330
13.3.1.1 Cube-Free Mediän Graphs 332
13.3.1.2 Q4-Free Mediän Graphs 333
13.3.1.3 Mediän Grid Graphs 333
13.3.2 Euler-Type Inequalities for Quasi-Median Graphs 334
13.3.3 Euler-Type Inequalities for Partial Cubes 335
13.3.4 Treelike Equality for Cage-Amalgamation Graphs 336
13.4 Cube Polynomials 337
13.4.1 Cube Polynomials of Cube-Free Mediän Graphs 339
13.4.2 Roots of Cube Polynomials 340
13.4.2.1 Rational Roots of Cube Polynomials 340
13.4.2.2 Real Roots of Cube Polynomials 341
13.4.2.3 Graphs of Acyclic Cubical Complexes 341
13.4.2.4 Product Mediän Graphs 342
13.4.3 Higher Derivatives of Cube Polynomials 342
13.5 Hamming Polynomials 343
13.5.1 A Different Type of Hamming Polynomial
for Cage-Amalgamation Graphs 344
13.6 Maximal Cubes in Mediän Graphs ofCircular Split Systems 345
13.7 Applications in Phylogenetics 346
13.8 Summary and Conclusion 347
References 348
Contents I XI
14 Elementary Elliptic (/?, q)-Polycycles 351
Michel Deza, Mathieu Dutour Sikiric, and Mikhail Shtogrin
14.1 Introduction 351
14.2 Kernel Elementary Polycycles 355
14.3 Classifkation of Elementary ({2, 3,4, 5}, 3)-Polycycles 356
14.4 Classifkation of Elementary ({2, 3}, 4)-Polycycles 359
14.5 Classifkation of Elementary ({2,3}, 5)-Polycycles 359
14.6 Conclusion 361
Appendix 1: 204 Sporadic Elementary ({2,3,4,5},3)-Polycycles 364
Appendix 2: 57 Sporadic eLementary ({2, 3}, 5)-polycycles 371
References 375
15 Optimal Dynamic Flows in Networks and Algorithms
for Finding Them 377
Dmitrii Lozovanu and Maria Fonoberova
15.1 Introduction 377
15.2 Optimal Dynamic Single-Commodity Flow Problems
and Algorithms for Solving Them 378
15.2.1 The Minimum Cost Dynamic Flow Problem 378
15.2.2 The Maximum Dynamic Flow Problem 380
15.2.3 Algorithms for Solving the Optimal Dynamic Flow Problems 380
15.2.4 The Dynamic Model with Flow Storage at Nodes 384
15.2.5 The Dynamic Model with Flow Storage at Nodes
and Integral Constant Demand-Supply Functions 384
15.2.6 Approaches to Solving Dynamic Flow Problems
with Different Types of Cost Functions 386
15.2.7 Determining the Optimal Dynamic Flows in Networks
with Transit Functions That Depend on Flow and Time 390
15.3 Optimal Dynamic Multicommodity Flow Problems
and Algorithms for Solving Them 392
15.3.1 The Minimum Cost Dynamic Multicommodity
Flow Problem 392
15.3.2 Algorithm for Solving the Minimum Cost Dynamic
Multicommodity Flow Problem 394
15.4 Conclusion 398
References 398
16 Analyzing and Modeling European R .D Collaborations:
Challenges and Opportunities from a Large Social Network 401
Michael J. Barber, Manfred Paier, and Thomas Schemgell
16.1 Introduction 401
16.2 Data Preparation 402
16.3 Network Definition 404
XII I Contents
16.4 Network Structure 405
16.5 Community Structure 407
16.5.1 Modularity 408
16.5.2 Finding Communities in Bipartite Networks 409
16.6 Communities in the Framework Program Networks 409
16.6.1 Topical Profiles of Communities 411
16.7 Binary Choice Model 413
16.7.1 The Empirical Model 413
16.7.2 Variable Construction 425
16.7.2.1 The Dependent Variable 415
16.7.2.2 Variables Accounting for Geographical Effects 415
16.7.2.3 Variables Accounting for FP Experience of Organizations 415
16.7.2.4 Variables Accounting for Relational Effects 416
16.7.3 Estimation Results 417
16.8 Summary 420
References 421
17 Analytic Combinatorics on Random Graphs 425
Michael Drmota and Bernhard Cittenberger
17.1 Introduction 425
17.2 Trees 426
17.2.1 The Degree Distribution 429
17.2.2 The Height 430
17.2.3 The Profile 431
17.2.4 TheWidth 434
17.3 Random Mappings 436
17 .4 The Random Graph Model of Erdös and Renyi 438
17.4.1 Counting Connected Graphs with Wright's Method 438
17.4.2 Emergence of the Giant Component 440
17.5 Planar Graphs 445
References 449
Index 457
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| spelling | Analysis of complex networks from biology to linguistics ed. by Matthias Dehmer ... Weinheim WILEY-VCH 2009 XVIII, 462 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graph theory Information networks Mathematical analysis Bioinformatik (DE-588)4611085-9 gnd rswk-swf Bioinformatik (DE-588)4611085-9 s DE-604 Dehmer, Matthias 1968- Sonstige (DE-588)129565245 oth text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3192174&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017325316&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Analysis of complex networks from biology to linguistics Graph theory Information networks Mathematical analysis Bioinformatik (DE-588)4611085-9 gnd |
| subject_GND | (DE-588)4611085-9 |
| title | Analysis of complex networks from biology to linguistics |
| title_auth | Analysis of complex networks from biology to linguistics |
| title_exact_search | Analysis of complex networks from biology to linguistics |
| title_full | Analysis of complex networks from biology to linguistics ed. by Matthias Dehmer ... |
| title_fullStr | Analysis of complex networks from biology to linguistics ed. by Matthias Dehmer ... |
| title_full_unstemmed | Analysis of complex networks from biology to linguistics ed. by Matthias Dehmer ... |
| title_short | Analysis of complex networks |
| title_sort | analysis of complex networks from biology to linguistics |
| title_sub | from biology to linguistics |
| topic | Graph theory Information networks Mathematical analysis Bioinformatik (DE-588)4611085-9 gnd |
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