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SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL

This talk presents a mathematical model analyzing the sensitivity of social network dynamics to noise variance. By examining scenarios with varying degrees of influence among agents and observable characteristics, we explore how noise affects clustering behavior in social networks. Results show distinctions between deterministic outcomes and those influenced by added noise. The discussion includes numerical results, conclusions, and future research directions, emphasizing model flexibility and sensitivity analysis within evolving networks.

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SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL

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  1. SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL Hoan K. Nguyen Center for Research in Scientific Computation North Carolina State University LVSS Transition Workshop SAMSI November 10-11, 2005 Collaborators: H.T Banks, A.F. Karr, and J.R. Samuels, Jr.

  2. TALK OVERVIEW • Mathematical Model • An Example • Numerical Results • Conclusions and Future work

  3. SOCIAL NETWORK MODEL Nodes (Agents) • observed characteristics

  4. MATHEMATICAL MODEL where • : number of elements in • : degree of influence that exert on

  5. CHARACTERIZE MODEL BEHAVIOR: FANTASY OR REALITY? Noise Dominated ?? ?? Noise Enriched Noise Enlarged ?? Essentially Deterministic

  6. AN EXAMPLE • 10 agents (A1, A2,…,AN) • Each agent has 2 observable characteristics • Sociability quotient ( ) : -10 (loners) 10 (people lovers) • Outlook on life ( ) : -10 (negative outlook) 10 (positive outlook) • determine different clustering scenarios • : 1 cluster; : 2 clusters; : 3 clusters

  7. TWO CLUSTER SENARIO

  8. THREE CLUSTER SCENARIO

  9. ONE CLUSTER SCENARIO

  10. REGIME DEFINITION • Fix to have single cluster scenario • Essentially Deterministic: • Both fate and path are as in the deterministic case • Noise Enriched: • Fate is the same as the deterministic case, but the set of paths is bigger • Noise Enlarged: • If fate is either a two cluster or a three cluster scenario described above • Noise Dominated: • No structured behavior at all

  11. NOISE ENRICHED SAMPLES Agent 2 Agent 7

  12. MORE NOISE ENRICHED SAMPLES Agent 6 Agent 10

  13. CONCLUSIONS AND FUTURE WORK • is more sensitive to the regime than • Noise Enlarged regime does not exist • Model richness and flexibility (e.g., ) • Sensitivity Analysis • Model Generalizations • Links that are born and die • Overlaid network (multi-dimensional links)

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