General Threshold and Cascade Models Lecture 2-4 General Threshold and Cascade Models Weili Wu Ding-Zhu Du University of Texas at Dallas First, I want to thank you for you presence. ********In this presentation I will try to introduce The social network which is a theoretical structure to study relationships between individuals, groups, organizations, or even entire societies. It is related to a wide range of disciplines. These disciplines include, but are not limited to information science, biology, economics, geography, communication studies, and so on.. The study of social networks begins with the late eighteenth century, two sociologists (Émile [ei'mi:l] Durkheim and Ferdinand ['fɝdənænd] Fer迪南de Tönnies) foreshadowed the idea of social networks in their theories and research of social groups. Nowadays, we study social networks using network analysis to identify social communities, pick influential person, and design good software.
Outline General Threshold Model General Cascade Model σGT(A)=σGC(A) 1. Brief overview of social networks 2. How to build applications on top of the social network – Think about a social network being MS Windows, We can build applications on it.
General Threshold Model
General Threshold Model 1 2 3
LT: Stop! w v Y Inactive Node 0.6 Active Node 0.2 Threshold 0.2 0.3 Active neighbors X 0.1 0.4 U 0.3 0.5 Stop! 0.2 0.5 w v
Outline General Threshold Model General Cascade Model σGT(A)=σGC(A) 1. Brief overview of social networks 2. How to build applications on top of the social network – Think about a social network being MS Windows, We can build applications on it.
General Cascade Model 1 2 3 Order-independentce Assumption
Explanation of 3 Theorem
IC: Y 0.6 Inactive Node 0.2 0.2 0.3 Active Node Newly active node X U 0.1 0.4 Successful attempt 0.5 0.3 0.2 Unsuccessful attempt 0.5 w v Stop!
MC: Y 0.6 Inactive Node 0.2 0.2 0.3 Active Node Newly active node X U 0.1 0.4 Successful attempt 0.5 0.3 0.2 Unsuccessful attempt 0.5 w v Stop!
Is the MC model a special case of General Cascade model?
Outline General Threshold Model General Cascade Model σGT(A)=σGC(A) 1. Brief overview of social networks 2. How to build applications on top of the social network – Think about a social network being MS Windows, We can build applications on it.
Equivalence Theorem Proof 1 2
Proof of 1 Is it well-defined?
General Threshold
General Cascade ？
Proof of 2
General Cascade
General Threshold
References
Welcome to Submit Papers A New Springer Journal Computational Social Networks Editor-in-Chief: Ding-Zhu Du My T. Thai Social network analysis [SNA] is the mapping and measuring of relationships and flows between people, groups, organizations, computers or other information/knowledge processing entities. The nodes in the network are the people and groups while the links show relationships or flows between the nodes. The advantage of social network analysis is that, unlike many other methods, it focuses on interaction (rather than on individual behavior). Network analysis allows us to examine how the configuration of networks influences how individuals and groups, organizations, or systems function. Welcome to Submit Papers
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