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Agent-Based Methods for Dynamic Social Networks

This presentation examines the dynamics of social networks through agent-based modeling. Conducted by Eric Vance at Duke University's Graduate Student Research Day in April 2006, it highlights how social relationships evolve over time, the detection of patterns, and predictive modeling. By establishing simple rules for agents in simulations, the research illustrates how complex social phenomena emerge from individual interactions. The study focuses on a practical application, analyzing friendship formation among students in a boarding school setting and investigating the impact of social proximity and characteristics.

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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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