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Table of Contents
Intro; Contents; Part I Introduction to Spreading in Social Systems; Complex Contagions: A Decade in Review; 1 Introduction; 2 Empirical Advances; 2.1 Applications to Health; 2.2 Diffusion of Innovations; 2.3 Social Media; 2.4 Politics; 3 Theoretical Advances; 4 New Directions; 4.1 Ecologies of Complex Contagions; 4.2 Mapping Heterogeneous Thresholds in Context; 4.3 The Roles of Homophily and Diversity in Diffusion; 5 Conclusion; References; A Simple Person's Approach to Understanding the Contagion Condition for Spreading Processes on Generalized Random Networks; 1 Introduction.
2 Elements of Simple Contagion on Random Networks3 The Contagion Condition; 3.1 Contagion Condition for One-Shot Spreading Processes; 3.2 Contagion Condition for Multiple-Shot Spreading Processes; 3.3 Remorseless Spreading and the Giant Component Condition; 3.4 Simple Contagion on Generalized Random Networks; 3.5 Other Routes to Determining the Contagion and Giant Component Conditions; 3.6 Simple Contagion on Generalized Directed Random Networks; 3.7 Simple Contagion on Mixed, Correlated Random Networks; 3.8 Contagion on Correlated Random Networks with Arbitrary Node and Edge Types.
3.9 Simple Contagion on Bipartite Random Networks3.10 Threshold Contagion on Generalized Random Networks; 3.11 Connecting the Contagion Condition for All-To-All and Random Networks for Threshold Contagion; 4 Concluding Remarks; References; Challenges to Estimating Contagion Effects from Observational Data; 1 Background; 2 Motivating Example; 3 Defining Causal Effects; 4 Confounding; 4.1 Homophily; 4.2 Shared Environment; 5 Dependence; 5.1 Sources of Network Dependence; 6 Solutions; 6.1 Randomization; 6.2 Parametric Models; 6.3 Instrumental Variable Methods.
6.4 Data from Multiple Independent Networks6.5 Highly Structured Dependence; 7 Conclusion; References; Part II Models and Theories; Slightly Generalized Contagion: Unifying Simple Models of Biological and Social Spreading; 1 Introduction; 2 Independent Interaction Models of Biological Contagion; 3 Interdependent Interaction Models of Social Contagion; 4 Generalized Contagion Model; 5 Analysis; 6 Concluding Remarks; References; Message-Passing Methods for Complex Contagions; 1 Introduction; 2 Configuration-Model Networks; 2.1 Naive Mean-Field Approximation.
2.2 Message-Passing for Configuration-Model Networks2.3 The Criticality Condition (i.e., ``Cascade Condition''); 3 Networks with Degree-Degree Correlations; 3.1 Matrix Criticality Condition; 4 Message-Passing for Finite-Size Networks; 4.1 Criticality Condition for Finite-Size Networks; 5 Conclusions; References; Optimal Modularity in Complex Contagion; 1 Introduction; 2 Analytical Framework; 2.1 Mean-Field and Message-Passing Approaches for Configuration Model; 2.2 Generalization to Modular Networks; 3 Networks with Two Communities; 4 Optimal Modularity in Networks with Many Communities.
2 Elements of Simple Contagion on Random Networks3 The Contagion Condition; 3.1 Contagion Condition for One-Shot Spreading Processes; 3.2 Contagion Condition for Multiple-Shot Spreading Processes; 3.3 Remorseless Spreading and the Giant Component Condition; 3.4 Simple Contagion on Generalized Random Networks; 3.5 Other Routes to Determining the Contagion and Giant Component Conditions; 3.6 Simple Contagion on Generalized Directed Random Networks; 3.7 Simple Contagion on Mixed, Correlated Random Networks; 3.8 Contagion on Correlated Random Networks with Arbitrary Node and Edge Types.
3.9 Simple Contagion on Bipartite Random Networks3.10 Threshold Contagion on Generalized Random Networks; 3.11 Connecting the Contagion Condition for All-To-All and Random Networks for Threshold Contagion; 4 Concluding Remarks; References; Challenges to Estimating Contagion Effects from Observational Data; 1 Background; 2 Motivating Example; 3 Defining Causal Effects; 4 Confounding; 4.1 Homophily; 4.2 Shared Environment; 5 Dependence; 5.1 Sources of Network Dependence; 6 Solutions; 6.1 Randomization; 6.2 Parametric Models; 6.3 Instrumental Variable Methods.
6.4 Data from Multiple Independent Networks6.5 Highly Structured Dependence; 7 Conclusion; References; Part II Models and Theories; Slightly Generalized Contagion: Unifying Simple Models of Biological and Social Spreading; 1 Introduction; 2 Independent Interaction Models of Biological Contagion; 3 Interdependent Interaction Models of Social Contagion; 4 Generalized Contagion Model; 5 Analysis; 6 Concluding Remarks; References; Message-Passing Methods for Complex Contagions; 1 Introduction; 2 Configuration-Model Networks; 2.1 Naive Mean-Field Approximation.
2.2 Message-Passing for Configuration-Model Networks2.3 The Criticality Condition (i.e., ``Cascade Condition''); 3 Networks with Degree-Degree Correlations; 3.1 Matrix Criticality Condition; 4 Message-Passing for Finite-Size Networks; 4.1 Criticality Condition for Finite-Size Networks; 5 Conclusions; References; Optimal Modularity in Complex Contagion; 1 Introduction; 2 Analytical Framework; 2.1 Mean-Field and Message-Passing Approaches for Configuration Model; 2.2 Generalization to Modular Networks; 3 Networks with Two Communities; 4 Optimal Modularity in Networks with Many Communities.