社会网络上的观点传播：建模与分析
发布时间：2021-08-03 02:31
传播过程的建模与分析,由于其在生物学、经济学和社会科学等领域的广泛应用受到众多研究者的关注与青睐。目前,大多数传播问题的研究主要集中在只具有合作交互关系的网络上。通常,观点的传播会受到个体之间交互形式的影响。本文着重研究观点在符号网络上传播的建模与分析。符号网络可以有效地刻画社会网络中个体之间的合作（信任的/友好的）与对抗（不信任的/敌对的）交互。主要研究内容如下:1.研究了多个相互竞争的观点在符号网络上的传播问题。网络中的个体改变自己观点的方式是以一定概率坚持自己前一时刻的观点或随机选择他/她的一个邻居来确定自己的观点。如果个体所选择的邻居是以合作方式与其交互的,他/她将采纳这个邻居的观点;如果邻居与其是对抗交互的,个体则以非均匀概率或均匀概率从多个相互竞争的观点中选择一个与其邻居不同的观点。根据上述更新规则,我们提出了两个传播模型。为了分析非均匀概率情形下的传播模型,我们构造了一个新的网络,并说明了它与符号网络之间的联系。利用两个网络之间的联系,给出了该传播模型收敛的充分条件。对于均匀概率情形下的传播模型,我们给出了在网络拓扑方面该模型收敛的充分必要条件。另外,如果符号网络是结构平...
【文章来源】：西安电子科技大学陕西省 211工程院校 教育部直属院校
【文章页数】：102 页
【学位级别】：博士
【文章目录】：
ABSTRACT
摘要
Chapter 1 Introduction
1.1 Background
1.2 Motivation
1.3 Literature Review
1.3.1 Propagation Problem
1.3.2 Competitive Diffusion Problem
1.4 Organization and Contribution of the Thesis
Chapter 2 Preliminaries
2.1 Notation and Special Matrices
2.2 Matrix Theory
2.3 Graph Theory
2.3.1 Signed Graph
2.3.2 Main Lemmas
Chapter 3 Competing Opinion Propagation over Signed Networks: Convergence Analysis
3.1 Introduction
3.2 Model Description
3.3 Main Results
3.3.1 Convergence Analysis of the Propagation Models
3.3.2 Further Results over Structurally Balanced Networks
3.4 Simulations
3.5 Summary
Chapter 4 Competitive Diffusion in Signed Networks: A Game-Theoretic Perspective
4.1 Introduction
4.2 Problem Statement
4.2.1 Propagation Model with Stubborn Individuals
4.2.2 Game Model
4.3 Main Results
4.3.1 Nash Equilibrium of the Game
4.3.2 Structurally Balanced Networks
4.4 Simulations
4.5 Summary
Chapter 5 Binary Opinion Propagation over Signed Networks: Equilibrium Analysis
5.1 Introduction
5.2 Model Description
5.2.1 An Approximation to the Discrete SIS Model
5.2.2 The Propagation Model
5.3 Main Results
5.3.1 The Analysis on Zero Equilibrium of Propagation Model
5.3.2 The Analysis on Nonzero Equilibrium of Propagation Model
5.4 Simulations
5.5 Summary
Chapter 6 Conclusions and Future Research
6.1 Conclusions
6.2 Future Work
Reference
Acknowledgement
Biography
本文编号：3318745
【文章来源】：西安电子科技大学陕西省 211工程院校 教育部直属院校
【文章页数】：102 页
【学位级别】：博士
【文章目录】：
ABSTRACT
摘要
Chapter 1 Introduction
1.1 Background
1.2 Motivation
1.3 Literature Review
1.3.1 Propagation Problem
1.3.2 Competitive Diffusion Problem
1.4 Organization and Contribution of the Thesis
Chapter 2 Preliminaries
2.1 Notation and Special Matrices
2.2 Matrix Theory
2.3 Graph Theory
2.3.1 Signed Graph
2.3.2 Main Lemmas
Chapter 3 Competing Opinion Propagation over Signed Networks: Convergence Analysis
3.1 Introduction
3.2 Model Description
3.3 Main Results
3.3.1 Convergence Analysis of the Propagation Models
3.3.2 Further Results over Structurally Balanced Networks
3.4 Simulations
3.5 Summary
Chapter 4 Competitive Diffusion in Signed Networks: A Game-Theoretic Perspective
4.1 Introduction
4.2 Problem Statement
4.2.1 Propagation Model with Stubborn Individuals
4.2.2 Game Model
4.3 Main Results
4.3.1 Nash Equilibrium of the Game
4.3.2 Structurally Balanced Networks
4.4 Simulations
4.5 Summary
Chapter 5 Binary Opinion Propagation over Signed Networks: Equilibrium Analysis
5.1 Introduction
5.2 Model Description
5.2.1 An Approximation to the Discrete SIS Model
5.2.2 The Propagation Model
5.3 Main Results
5.3.1 The Analysis on Zero Equilibrium of Propagation Model
5.3.2 The Analysis on Nonzero Equilibrium of Propagation Model
5.4 Simulations
5.5 Summary
Chapter 6 Conclusions and Future Research
6.1 Conclusions
6.2 Future Work
Reference
Acknowledgement
Biography
本文编号：3318745
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