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

SAMSINovember 10-11, 2005

Collaborators: H.T Banks, A.F. Karr, and J.R. Samuels, Jr.

TALK OVERVIEW

• Mathematical Model

• An Example

• Numerical Results

• Conclusions and Future work

Nodes (Agents)

iA

jA

),,( tije),,( tjie

SOCIAL NETWORK MODEL

– observed characteristics )(tCi

MATHEMATICAL MODEL

ejiji

tNj

Ciji

i

ii

dWdttCtCftjide

WddttCtCN

tCdi

,

2

)(

)()( ),,(

)()()(

0b,12)( bef

)( };0),,(|{)( tNtjiejtN ii

where

• : number of elements in

• : degree of influence that exert on

)(tN i

)(tNA ij 0i iA

Essentially Deterministic

Noise Enriched

Noise Enlarged

Noise Dominated

??

??

??

CHARACTERIZE MODEL BEHAVIOR:

FANTASY OR REALITY?

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

outiC

1i

)5,5()0(7 C

sqiC

);10,10()0(2 C

),10,10()0( iC

;7,2i

0)0,,( jie

0b

)033.0,0(b ]105.0,033.0[b),105.0( b

TWO CLUSTER SENARIO

THREE CLUSTER SCENARIO

ONE CLUSTER SCENARIO

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

0165.0b

NOISE ENRICHED SAMPLES

Agent 2 Agent 7

MORE NOISE ENRICHED SAMPLES

Agent 6 Agent 10

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)

j

Ciji

j

ii dWdttCtCtjie

tjietCd

)()(),,(),,(

)(

im

iibb ;;