Evolutionary Dynamics of Complex Communications Networks

318 Pages·2013·5.689 MB·English

by  Vasileios Karyotis, Eleni Stai, Symeon Papavassiliou

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Evolutionary Dynamics
of Complex
Communications
Networks
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Evolutionary Dynamics
of Complex
Communications

Networks
Vasileios Karyotis
Eleni Stai
Symeon Papavassiliou
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CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2014 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
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Version Date: 20130806
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Contents
Preface ix

1 Introduction 1
1.1 Approach and Objectives . . . . . . . . . . . . . . . . . . . . . 2
1.2 Fundamentals of Complex Networks . . . . . . . . . . . . . . . 5
1.2.1 Complex Networks Fundamentals . . . . . . . . . . . . . 10
1.2.2 Complex Network Taxonomy and Examples . . . . . . . 12
1.3 Network Science . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.1 Content and Promise of Network Science . . . . . . . . 21
1.3.2 Networks and Network Research in the 21st Century . . 23
1.3.3 Status and Challenges of Network Science . . . . . . . . 25
2 Basic Network Graph Models and Their Properties 29
2.1 Graph Theory Fundamentals . . . . . . . . . . . . . . . . . . . 30
2.1.1 Basic Definitions and Notation . . . . . . . . . . . . . . 31
2.1.2 Additional Definitions . . . . . . . . . . . . . . . . . . . 35
2.1.3 Connectivity . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.4 Paths and Cycles . . . . . . . . . . . . . . . . . . . . . . 46
2.1.5 Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.1.6 Planarity . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.1.7 Coloring (Covering) . . . . . . . . . . . . . . . . . . . . 53
2.1.8 Algebraic Graph Theory . . . . . . . . . . . . . . . . . . 55
2.2 Random Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2.1 Basic Random Graph Models . . . . . . . . . . . . . . . 60
2.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 Cognitive Methods and Evolutionary Computing 65
3.1 Brief History of Evolutionary Computing . . . . . . . . . . . . 66
3.2 Elements from Evolution Theory . . . . . . . . . . . . . . . . . 66
3.3 Evolutionary Computing . . . . . . . . . . . . . . . . . . . . . . 68
3.3.1 Components of Evolutionary Algorithms . . . . . . . . . 70
3.3.2 Representation . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.3 Fitness Function . . . . . . . . . . . . . . . . . . . . . . 73
v
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vi Contents
3.3.4 Population . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.5 Parent Selection . . . . . . . . . . . . . . . . . . . . . . 74
3.3.6 Variation Operators: Recombination and Mutation . . . 74
3.3.7 Survivor Selection . . . . . . . . . . . . . . . . . . . . . 75
3.3.8 Initialization and Termination Conditions . . . . . . . . 75
3.3.9 Operation of Evolutionary Algorithm . . . . . . . . . . 76
3.4 Evolutionary Computing Approaches . . . . . . . . . . . . . . . 79
3.4.1 Genetic Algorithms. . . . . . . . . . . . . . . . . . . . . 79
3.4.2 Evolutionary Strategy . . . . . . . . . . . . . . . . . . . 91
3.4.3 Genetic Programming . . . . . . . . . . . . . . . . . . . 95
3.4.4 Evolutionary Programming . . . . . . . . . . . . . . . . 98
3.4.5 Evolutionary Computing at a Glance . . . . . . . . . . . 100
3.4.6 Parameter Control in Evolutionary Algorithms . . . . . 100
3.4.7 Special Forms of Evolution . . . . . . . . . . . . . . . . 105
4 Complex and Social Network Analysis Metrics and
Features 109
4.1 Degree Distribution . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 Average Path Length . . . . . . . . . . . . . . . . . . . . . . . . 114
4.4 Clustering Coefficient . . . . . . . . . . . . . . . . . . . . . . . 115
4.4.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.4.2 Extension to Weighted Graphs . . . . . . . . . . . . . . 116
4.4.3 Extension to Directed Graphs . . . . . . . . . . . . . . . 118
4.5 Centrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5.1 Degree Centrality. . . . . . . . . . . . . . . . . . . . . . 123
4.5.2 Closeness (Path) Centrality . . . . . . . . . . . . . . . . 125
4.5.3 Betweenness Centrality . . . . . . . . . . . . . . . . . . 128
4.5.4 Betweenness Centrality Approximation Methods . . . . 130
4.5.5 Eigenvector Centrality . . . . . . . . . . . . . . . . . . . 135
4.5.6 Example of Centralities’ Computation . . . . . . . . . . 136
4.6 Prestige . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.6.1 Degree Prestige . . . . . . . . . . . . . . . . . . . . . . . 139
4.6.2 Influence Domain . . . . . . . . . . . . . . . . . . . . . . 139
4.6.3 Proximity Prestige . . . . . . . . . . . . . . . . . . . . . 140
4.7 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.8 Metrics at a Glance . . . . . . . . . . . . . . . . . . . . . . . . 143
5 Distinctive Structure and Features of Complex Networks 145
5.1 Network Structure and Evolution . . . . . . . . . . . . . . . . . 145
5.2 Small-world Paradigm . . . . . . . . . . . . . . . . . . . . . . . 146
5.2.1 Prolegomena—Description of a Small-World Network . 146
5.2.2 Large-scale Experiments—“Six Degrees of Separation” . 148
5.2.3 Watts and Strogatz Model (WS Model) . . . . . . . . . 150
5.2.4 Kleinberg’s Model . . . . . . . . . . . . . . . . . . . . . 153
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Contents vii
5.2.5 Examples and Applications . . . . . . . . . . . . . . . . 155
5.3 Scale-free Networks . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.3.1 Definition and Properties . . . . . . . . . . . . . . . . . 158
5.3.2 Examples and Applications . . . . . . . . . . . . . . . . 161
5.3.3 Barab´asi–Albert Model . . . . . . . . . . . . . . . . . . 162
5.3.4 Extensions of the Barab´asi–Albert Model . . . . . . . . 168
5.4 Hyperbolic Structure of Complex Networks . . . . . . . . . . . 176
5.4.1 Background on Hyperbolic Geometry . . . . . . . . . . 176
5.4.2 Evolutionary Models Developed on Hyperbolic
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5 Expansion Properties. . . . . . . . . . . . . . . . . . . . . . . . 180
5.5.1 Definition and Analytical Properties . . . . . . . . . . . 180
5.5.2 Applications of Expander Graphs . . . . . . . . . . . . . 184
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6 Evolutionary Approaches 187
6.1 A Brief Description of Wireless Multi-hop Communications . . 188
6.2 Topology Control (TC) and Inverse Topology Control (iTC) . . 191
6.3 Spatial Graphs and Small-World Phenomenon . . . . . . . . . . 192
6.4 Inverse Topology Control-Based Approaches . . . . . . . . . . . 195
6.4.1 Early Approaches Using Wired Shortcuts . . . . . . . . 196
6.4.2 Approaches Using Wireless Shortcuts . . . . . . . . . . 202
6.5 Holistic Topology Modification Framework . . . . . . . . . . . . 208
6.5.1 Weighted Edge Churn Framework . . . . . . . . . . . . 209
6.5.2 Weighted Node Churn Framework . . . . . . . . . . . . 216
6.5.3 Combined Mechanism (WEC and WNC) . . . . . . . . 220
6.5.4 Optimization Methodology . . . . . . . . . . . . . . . . 221
6.6 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.6.1 Example 1: Elimination to Binary Graphs (SETM) . . . 229
6.6.2 Example 2: Trust Management in Wireless Multi-Hop
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
7 Conclusion 247
7.1 Lessons Learned . . . . . . . . . . . . . . . . . . . . . . . . . . 247
7.1.1 Emerging Trends and Their Benefits . . . . . . . . . . . 248
7.1.2 Discussion on Evolutionary Topology Modification
Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 251
7.2 The Road Ahead . . . . . . . . . . . . . . . . . . . . . . . . . . 251
7.2.1 Route Covered Already . . . . . . . . . . . . . . . . . . 251
7.2.2 Open Problems . . . . . . . . . . . . . . . . . . . . . . . 253
7.3 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Appendices 257
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viii Contents
A Geometric Probability 259
A.1 Probability Theory Elements . . . . . . . . . . . . . . . . . . . 259
A.2 Probabilistic Modeling of the Deployment of a Wireless Multi-
Hop Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
B Semirings and Path Problems 263
B.1 Monoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
B.2 Semirings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
B.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
References 267
Author Index 277

Subject Index 283
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Preface
In this book, we start the exploration of evolutionary dynamics for complex
networkswithaworkingexamplethatmightlookfamiliartomanypeople,at
least partially. The specific example intends to highlight the various aspects
of everyday life and work where humans encounter, use, act on and obtain
information from their interaction with complex communications networks,
as well as numerous other emerging functions. Such an example will drive
the following steps of the exploration of this book into a research domain
currently shaping and even expanding rapidly. Then we provide a more elab-
oratedoverviewofthetopic,relatedgoals,andfeaturesprovidedbythisbook.
Finally, we provide potential alternative strategies for studying the material
provided, depending on whether the book is intended as a research reference,
an undergraduate or graduate course reference manual, or simply a reference
of broader interest.
Working Example
An executive of a multi-national company hires a taxi from Tokyo Financial
CentertogotowardstheInternationalairport,tocatchherreturnflighttothe
United States. The driver quickly consults the GPS device of the vehicle for
thetrafficstreetmap,inordertoidentifythefastestroutetotheairport.The
executive has requested a speedy lift, which will ensure she boards on time.
Theroutedurationestimationis40min,safelyenablingtheexecutivetocheck
her email through her mobile handheld device in the meantime, rather than
worryaboutcatchingherflight.BoththeaccuracyoftheGPSapplicationand
theluxuryofagoodinternationalroamingplanallowhertofocusonherjob,
whilenotwastingenergyonlogistics.Thelatestemailrequireshertocomplete
areport,thus,shealsoopensuphertabletdevice,connectstothe4Gnetwork
of the local provider, and via roaming and VPN, she connects safely to the
intranet of her corporation, in order to complete the short report online and
make it accessible to her supervisor in Philadelphia as soon as possible.
Incidentally,assoonasthetaxireachestheairport,theexecutivereceives
an emergency call, informing her that she needs to reschedule her flight and
visitthecorporateofficesinLosAngelesforacoupleofdaysbeforereturning
ix
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