Social Networks: Modeling and Analysis

Description

The goal of this book is to provide a reference for applications of mathematical modeling in social media and related network analysis and offer a theoretically sound background with adequate suggestions for better decision-making. Social Networks: Modeling and Analysis provide the essential knowledge of network analysis applicable to real-world data, with examples from today's most popular social networks such as Facebook, Twitter, Instagram, YouTube, etc. The book provides basic notation and terminology used in social media and its network science. It covers the analysis of statistics for social network analysis such as degree distribution, centrality, clustering coefficient, diameter, and path length. The ranking of the pages using rank algorithms like Page Rank and HITS are also discussed. Written as a reference this book is for Engineering and Management Students, Research Scientists, Academicians involved in complex networks, mathematical sciences, and marketing research. Cover Half Title Title Page Copyright Page Dedication Contents Preface Acknowledgements Authors Chapter 1: Introduction to Social Networks 1.1. Concept of Complex Networks 1.2. Overview of Social Network Analysis 1.2.1. Social Networks and Social Networking 1.2.2. Social Network Visualization and Statistical Analysis 1.2.3. Social Network Modelling 1.2.4. Link Prediction 1.2.5. Community Detection 1.2.6. Ego Network 1.2.7. Network Motifs 1.2.8. Security and Privacy Issues 1.3. Social Media Content 1.3.1. Content Characteristics 1.3.2. Content Dynamics 1.3.3. User Characteristics 1.4. Levels of Network Analysis 1.4.1. Micro-Level 1.4.2. Meso-Level 1.4.3. Macro-Level 1.5. Complex Networks 1.6. Problems for Self-Assessment References Chapter 2: Network Statistics and Related Concepts 2.1. Networks and Graphs 2.2. Different Types of Networks 2.2.1. Undirected Networks 2.2.2. Directed Networks 2.2.3. Self-Loops 2.2.4. Multigraph/Simple Graphs 2.2.5. Weighted Network 2.2.6. Complete Graph (Clique) 2.2.7. Bipartite Graph 2.3. Representation of the Networks 2.3.1. Adjacency Matrix 2.3.2. Real Networks are Sparse 2.3.3. Complete Graph 2.4. Network Properties 2.4.1. Node Degree 2.4.2. Average Degree 2.4.3. Degree Distribution 2.4.4. Paths and Distance in Graph 2.4.5. Shortest Path 2.4.6. Network Diameter 2.4.7. Average Path Length 2.4.8. Clustering Coefficient 2.5. Problems for Self-Assessment References Chapter 3: Network Models 3.1. Basic Features of Networks 3.1.1. Continuous Distribution 3.1.2. Discrete Distribution 3.2. Generative Models 3.2.1. Random Graph Models 3.2.2. Preferential Attachment Model 3.2.3. Small-World Model 3.3. Six Degrees of Separation 3.4. Problems for Self-Assessment References Chapter 4: Network Centrality 4.1. Centrality Measures Overview 4.2. Degree Centrality 4.3. Eigenvector Centrality 4.4. Katz Centrality 4.5. Betweenness Centrality 4.6. Closeness Centrality 4.7. Problems for Self-Assessment References Chapter 5: Link Analysis 5.1. Link Analysis in Web Mining 5.2. Ranking Algorithms 5.3. Hyperlink-Induced Topic Search (HITS) 5.4. Pagerank Algorithm 5.5. Problems for Self-Assessment References Chapter 6: Link Prediction 6.1. Overview of Link Prediction 6.2. Link Prediction Methods 6.2.1. Graph Distance 6.2.2. Common Neighbours 6.2.3. Jaccard’s Coefficient 6.2.4. Adamic/Adar (Frequency-Weighted Common Neighbours) 6.2.5. Preferential Attachment 6.2.6. Katz (Exponentially Damped Path Counts) 6.2.7. Hitting Time 6.2.8. Rooted (Personalized) PageRank 6.3. Other Metrics 6.3.1. Friends Measure 6.3.2. Cosine Similarity 6.3.3. Sørensen Index 6.3.4. Hub Promoted Index 6.3.5. Hub Depressed Index 6.3.6. Leicht–Holme–Newman Index 6.4. Prediction Performance Metrics 6.5. Problems for Self-Assessment References Chapter 7: Community Detection 7.1. Overview of Community 7.2. Taxonomy of Community Criteria 7.2.1. Node-Centric Community Detection 7.2.2. Group-Centric Community Detection 7.2.3. Network-Centric Community Detection 7.2.4. Hierarchy-Centric Community Detection 7.3. Community Evaluation 7.4. Problems for Self-Assessment References Chapter 8: Ego Networks 8.1. Overview of Ego Networks 8.2. Characteristics of Ego Networks 8.3. Ego Network Measures 8.3.1. Ego Network Density 8.3.2. Structural Holes 8.3.3. Brokerage 8.4. Problems for Self-Assessment References Chapter 9: Network Cohesion 9.1. Overview of Network Cohesion 9.2. Triadic Closure 9.3. Embeddedness 9.4. Density 9.5. Dyadic Relation 9.6. Reciprocity 9.7. Homophily 9.8. Transitivity 9.9. Bridges 9.10. Group-External and Group-Internal Ties 9.11. Krackhardt’s Graph Theoretical Dimensions of Hierarchy 9.12. Positions and Roles 9.13. Problems for Self-Assessment References Chapter 10: Information Diffusion 10.1. Overview of Information Diffusion 10.2. Explicit Networks 10.2.1. Herd Behaviour 10.2.2. Information Cascades 10.3. Implicit Networks 10.3.1. Diffusion of Innovations 10.3.2. Epidemical Models 10.4. Problems for Self-Assessment References Chapter 11: Security and Privacy in Social Networks 11.1. Introduction 11.2. Need of Privacy 11.3. Social Network Privacy Model 11.4. Basic Concepts in Data Privacy 11.4.1. K-Anonymity 11.4.2. L-Diversity 11.4.3. T-Closeness 11.5. Randomization 11.6. Slicing 11.7. Problems for Self-Assessment References Chapter 12: Social Network Analysis Tools 12.1. Overview of Social Network Analysis Tools 12.2. Various Tools 12.2.1. Gephi (Visualization and Basic Network Metrics) 12.2.2. NetLogo (Modelling Network Dynamics) 12.2.3. Igraph (for Programming Assignment) 12.2.4. Pajek (User Friendly, Free, Windows Only) 12.2.5. UCINET (Extensive, Socially Focused Functionality, Windows Only) 12.2.6. Network Overview Discovery Exploration for Excel (NodeXL) (SNA Integrated to Excel, Windows Only, Free, Beta) 12.2.7. NetMiner 4 12.2.8. NetworkX (Extensive Functionality, Scales to Large Networks by Taking Advantage of Existing C, Fortran Libraries for Large Matrix Computations, Open Source) 12.2.9. R (Extensive, Statistics-Heavy Functionality) 12.2.10. SocioViz 12.2.11. UNISoN (Social Network Analysis Tool) 12.2.12. Wolfram Alpha 12.3. Problems for Self-Assessment References Index