Bernoulli transmissions

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Table of contents

1 Random Graphs: an Overview 
1.1 Galton-Watson Branching Processes
1.2 Erd˝os-Rényi Random Graph
1.2.1 Phase transition: Emergence of a giant component
1.2.2 Connectivity
1.3 Configuration Model
1.3.1 Phase transition: Emergence of a giant component
1.3.2 Information diffusion
1.3.3 Connectivity
1.3.4 Diameter of weighted configuration model
1.4 Local weak convergence
2 Viral Marketing in Configuration Model 
2.1 Introduction
2.1.1 Enhanced Configuration Model
2.1.2 Results
2.1.3 Methodology
2.1.4 Related Work
2.2 Notation and Results
2.2.1 Forward influence propagation
2.2.2 Pioneers— Branching process heuristic
2.2.3 Dual Back-Propagation Process
2.2.4 Concluding Remarks
2.3 Analysis of the Original Forward-Propagation Process
2.4 Analysis of the Dual Back-Propagation Process
2.5 Duality Relation
3 Viral Marketing: Examples, Applications and Numerical Studies 
3.1 Introduction
3.1.1 Related Work
3.2 Examples
3.2.1 Bernoulli transmissions
3.2.2 Enthusiastic and apathetic users or node percolation
3.2.3 Absentminded users or coupon-collector transmissions
3.2.4 Numerical examples
3.2.4.1 Simulations
3.2.4.2 Estimation
3.2.4.3 Analytic evaluation
3.2.4.4 Case study
3.3 Application to Viral Campaign Evaluation
4 Isolated Vertices and the Longest Edge of the Minimum Spanning Tree of Weighted Configuration
4.1 Introduction
4.2 Results
4.3 Isolated vertices of weighted configuration model
4.4 Longest edge of MST
5 FutureWork: Convex comparison of Random Graphs 
5.1 Convex Comparison of Random Graphs
5.1.1 Convex Order on Galton-Watson Tree and Implications
5.1.2 Convex Order on Sequences of Finite Random Graphs and Implications in Configuration