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Agent-Based Methods for Dynamic Social Networks

Agent-Based Methods for Dynamic Social Networks. Eric Vance ISDS Duke University. Graduate Student Research Day April 5, 2006. Social Networks. Social Network analysis models relationships between actors. 1 signifies a friendship, 0 indicates the absence of a friendship. F AB =1

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Agent-Based Methods for Dynamic Social Networks

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  1. Agent-Based Methods for Dynamic Social Networks Eric Vance ISDS Duke University Graduate Student Research Day April 5, 2006

  2. Social Networks • Social Network analysis models relationships between actors. • 1 signifies a friendship, 0 indicates the absence of a friendship FAB=1 FAC=1 FBA=1 FBC=0 FCA=0 FCB=1 B A C

  3. Dynamic Social Networks • How do networks change over time? • How do we identify patterns? • How do we make predictions?

  4. Agent-based models • Program simple rules for agents in a computer simulation. • Complex phenomena can be generated by individual agents acting according to the simple rules. • Evaluate each new rule.

  5. Static Social Network Model • logit(pij)=0+s(si+rj)+ Xij-|zi-zj| • Intercept 0 is a baseline probability for friendship • Sender si random effect • Receiver rj random effect • Vector of dyad-specific (observable) covariates Xij • Positions (zi) in latent (unobservable) Social Space • The distance between zi and zj in Social Space affects the probability of a friendship from i  j. • Actors close together in social space are more likely to be friends.

  6. Our Approach--Motivation • Students arrive at a boarding school having no friends. • Each student occupies a position in Social Space. • Students make friends at each time according to simple rules which mimic the static social network model.

  7. Student Social Space • Social Space is a useful proxy for that which we cannot measure. • Students move towards their friends in Social Space. • Students change their habits and interests to be more similar to their friends’.

  8. Student Social Space B • Students close together have similar characteristics A Sports C Fashion

  9. 3 Rules for Agent Model • Students are endowed with a position (zi), Sexi=M or F, Charisma ci N(0,1). • Make friends according to probability pij: logit(pij)=0+s(ci+cj)+ Xij-|zi-zj| • Move 1/3 distance towards the average of friends’ positions. • What happens when 0, s, and  vary?

  10. Simulation

  11. Simulation

  12. Simulation Results

  13. Analysis of Results--ANOVA Table • Approximate as a linear model: Avg # friends = coef 0+ coef s+ coef || +  • The intercept 0 has a very large effect. The  coefficient has a small effect.

  14. Future Directions • Use the model to estimate parameters for a dynamic network with real data. • How to summarize a social network? • Add rules to better reflect reality.

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