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 Sports Fashion B A C
Students close together have similar characteristics

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 || + 
Deg. f
Sum Squares
p-value 0 1
122148
<2e-16 s
4138
||
172
1.2e-06
Residuals
4455
32504
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.