Information Spread in a Social Media Age: Modeling and Control

279 Pages·2021·16.929 MB·English

by  Michael Muhlmeyer, Shaurya Agarwal

Information Spread in
a Social Media Age

Information Spread in
a Social Media Age
Modeling and Control
Michael Muhlmeyer
Shaurya Agarwal
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Contents
Foreword xiii
Preface xv
Authors xvii
Acknowledgments xix
List of Figures xxi
List of Tables xxv
List of Codes xxvii
Symbols xxix
1 Introduction 1
1.1 Expressions of Information . . . . . . . . . . . . . . . . . . . 2
1.2 Why Information Spread Matters? . . . . . . . . . . . . . . . 5
1.3 Modern Information Spread Scenarios . . . . . . . . . . . . . 5
1.3.1 Global Communication During a Pandemic . . . . . . 6
1.3.2 Governments and Mass Panic . . . . . . . . . . . . . . 6
1.3.3 Shopping and Advertising . . . . . . . . . . . . . . . . . 7
1.3.4 Social or Political Campaigning . . . . . . . . . . . . . . 7
1.3.5 Misinformation, Disinformation, and Fake News . . . 8
1.4 Controllable Information Spread . . . . . . . . . . . . . . . . 9
1.5 How to Read This Book . . . . . . . . . . . . . . . . . . . . . 10
1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
I Understanding Social Networking Systems 13
2 Social Media in Popular Culture 15
2.1 The Topology of Social Media . . . . . . . . . . . . . . . . . 15
2.2 Social Networking Sites . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Twitter . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Facebook . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 LinkedIn. . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Content Sharing Sites . . . . . . . . . . . . . . . . . . . . . . 18
vii
viii Contents
2.4 Discussion Forums . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 News and Blogs . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Shopping and Reviews . . . . . . . . . . . . . . . . . . . . . 20
2.7 Games and Music . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.8 Hybrid Social Media . . . . . . . . . . . . . . . . . . . . . . . . 21
2.8.1 Internet Memes . . . . . . . . . . . . . . . . . . . . . . 22
2.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Social Theory and Networks 25
3.1 Philosophy, Science, and Information Spread . . . . . . . . . 25
3.1.1 The Ancient World . . . . . . . . . . . . . . . . . . . . 26
3.1.2 The Medieval World . . . . . . . . . . . . . . . . . . . 26
3.1.3 The Early Modern World . . . . . . . . . . . . . . . . . 27
3.1.4 The Contemporary World . . . . . . . . . . . . . . . . 28
3.2 Social Theory and Social Networks . . . . . . . . . . . . . . 29
3.3 Social Exchange Theory . . . . . . . . . . . . . . . . . . . . . 30
3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Social Network Relationships and Structures 33
4.1 Social Network Relationship Overview . . . . . . . . . . . . . 33
4.2 Core Social Network Relationships . . . . . . . . . . . . . . . 34
4.2.1 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.2 Directionality . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.3 Intermediary Relationships . . . . . . . . . . . . . . . 34
4.2.4 Complex Networks . . . . . . . . . . . . . . . . . . . . 35
4.3 Homophily and Filter Bubbles . . . . . . . . . . . . . . . . . 36
4.4 Dyadic Relationships and Reciprocity . . . . . . . . . . . . . . 37
4.5 Triads and Balanced Relationships . . . . . . . . . . . . . . . 38
4.6 Social Network Analysis Software . . . . . . . . . . . . . . . 39
4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 Social Network Analysis 43
5.1 Density and Structural Holes . . . . . . . . . . . . . . . . . . 43
5.2 Weak and Strong Ties . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Centrality and Distance . . . . . . . . . . . . . . . . . . . . . 46
5.4 Small World Networks . . . . . . . . . . . . . . . . . . . . . . 48
5.5 Clusters, Cohesion, and Polarization . . . . . . . . . . . . . . 50
5.6 The Adjacency Matrix . . . . . . . . . . . . . . . . . . . . . 52
5.6.1 Example: A Fencing Club Sociogram . . . . . . . . . . 53
5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
II Macroscopic Modeling and Information Spread 57
Contents ix
6 Modeling Basics 59
6.1 What is a Model? . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Models in Decision Making . . . . . . . . . . . . . . . . . . . 60
6.3 Standard Models . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4 Models, Assumptions, and Approximations . . . . . . . . . . 63
6.5 Mathematical Systems Modeling . . . . . . . . . . . . . . . . 64
6.6 Microscopic and Macroscopic Models . . . . . . . . . . . . . 64
6.7 Basic Steps to Develop a Mathematical Model . . . . . . . . 66
6.8 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.9 Modeling and the State-Space Representation . . . . . . . . . 67
6.10 Example 1: A Spring-Mass System . . . . . . . . . . . . . . . 70
6.11 Example 2: A Predator-Prey System . . . . . . . . . . . . . . . 71
6.12 Example 3: An RLC Circuit . . . . . . . . . . . . . . . . . . 73
6.13 Example 4: An Epidemic Model . . . . . . . . . . . . . . . . 74
6.14 Example 5: Vehicular Traffic Modeling . . . . . . . . . . . . 76
6.14.1 LWR and Greenshields’ Models for Traffic . . . . . . . . 77
6.14.2 ODE Approximation of LWR Model . . . . . . . . . . 78
6.15 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7 Epidemiology-Based Models for Information Spread 85
7.1 Epidemiology Models . . . . . . . . . . . . . . . . . . . . . . 85
7.1.1 The SIR Disease Spread Model . . . . . . . . . . . . . 86
7.1.2 The SEIR Disease Spread Model . . . . . . . . . . . . 89
7.1.3 Herd Immunity in Epidemiology . . . . . . . . . . . . 90
7.1.4 “Flattening the Curve” . . . . . . . . . . . . . . . . . . 91
7.1.5 Epidemiology Models as Analog Models . . . . . . . . 93
7.2 Information Spread Models: Overview and Conventions . . . 94
7.3 The Ignorant-Spreader Model . . . . . . . . . . . . . . . . . 95
7.4 The Ignorant-Spreader-Ignorant (ISI) Model . . . . . . . . . . 97
7.5 The Ignorant-Spreader-Recovered (ISR) Model . . . . . . . 99
7.6 Reproductive Number and Herd Immunity . . . . . . . . . . . 101
7.7 ISR Model for Social Media . . . . . . . . . . . . . . . . . . . 103
7.7.1 ISR Model for Social Media with Decay . . . . . . . . 106
7.8 ISCR Model for Contentious Information Spread . . . . . . . . 107
7.9 Hybrid ISCR Model . . . . . . . . . . . . . . . . . . . . . . . 115
7.10 ISSRR Model for Contentious Information . . . . . . . . . . . 121
7.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8 Stochastic Modeling of Information Spread 129
8.1 Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . 130
8.2 Deterministic and Stochastic Realizations of Processes . . . . . 131
8.3 Stochastic Modeling Considerations for Social Media Systems 132
8.4 Stochastic ISI Information Model . . . . . . . . . . . . . . . 133
8.5 Stochastic ISR Information Modeling and Social Media . . . 135
8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137