AgentBased Methods for Dynamic Social Networks

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Agent-Based Methods for Dynamic Social
Networks

• Eric Vance
• David Banks
• Duke University

National Defense and Homeland Security JSM August
6, 2006
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Social Networks

• Social Network analysis models relationships
  between actors.
• 1 signifies a friendship, 0 indicates the absence
  of a friendship

FAB1 FAC1 FBA1 FBC0 FCA0 FCB1
B
A
C
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Dynamic Social Networks

• How do networks change over time?
• Which features are stable, which are dynamic?
• How do we make predictions?

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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.

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Static Social Network ModelHoff, Raftery, and
Handcock (2002)

• logit(pij)?0?s(sirj)? 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.

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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.

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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.

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Student Social Space

• Students close together have similar
  characteristics

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Simulation
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Simulation
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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Graphs of Friendships
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3 Rules for Agent Model

• 1. Students are endowed with a position (zi),
• SexiM or F, Charisma ci ? N(0,1).
• 2. Make friends according to probability pij
  logit(pij)?0?s(cicj)? Xij-zi-zj
• 3. Move 1/3 distance towards the average of
  friends positions.

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Agent Model Parameters

• Agents make friends according to probability pij
• logit(pij)?0?s(cicj)? Xij-zi-zj
• ? ?0 is baseline probability of friendship
• ? ?s is sensitivity of friendships to charisma
• ? ? is sensitivity of friendships to Same Sex

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Evaluation Metrics

• 1. Number of Friendships (Dyad links)
• Completed Triads
• Triangles (incompleted triads)
• Number of singletons
• Distance moved in Social Space
• Number of Opposite Sex Friends
• Number of Clusters
• Shortest path length between nodes

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Simulation Results
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Simulation Results
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Analysis of Results

• 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.

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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.