Actor Allegiance and Blockmodel Strength J. T. Rigsby and Dr. J. L. - - PowerPoint PPT Presentation

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Actor Allegiance and Blockmodel Strength J. T. Rigsby and Dr. J. L. Solka rigsbyjt@nswc.navy.mil;solkajl@nswc.navy.mil Naval Surface Warfare Center Dahlgren Division Interface 2004 p.1/24 Agenda Blockmodel Necessity Allegiance Toy

SLIDE 1

Actor Allegiance and Blockmodel Strength

J. T. Rigsby and Dr. J. L. Solka

rigsbyjt@nswc.navy.mil;solkajl@nswc.navy.mil

Naval Surface Warfare Center Dahlgren Division

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SLIDE 2

Agenda

Blockmodel Necessity Allegiance Toy Example Real Example Conclusions

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SLIDE 3

Acknowledgments

This work is supported by the In-house Laboratory Independent Research (ILIR) program. We wish to acknowledge helpful discussions with Dr. David Marchette of NSWCDD.

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SLIDE 4

Blockmodel

D - directed graph E - edges(ties) V - vertexes(actors) P = {P1, ..., Pk} - Partitions B = {B1,1, B1,2, ..., Bn,n−1, Bn,n} - Blockmodel Bi,j , when i = j - ties from actors in partition i to partition j Bi,j , when i = j - internal ties between actors in partition i

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SLIDE 5

Necessity

Measure blockmodel strength change Estimate the true number of partitions Turn the time separated graphs into a single graph

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SLIDE 6

Allegiance

is the measure of how much an actor is helping his block Help: Having internal edges to other block members Hint(actor) =

i=NPi E(actor)

Not having external edges to non-blockmembers Hext(actor) = N − NPi −

i=NPi E(actor)

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SLIDE 7

Allegiance Equation

A(i) = α[Hint(i)] + (1 − α)[Hext(i)] α ∈ [0, 1] - weight function

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SLIDE 8

Toy Example

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SLIDE 9

Equivalence Cluster

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SLIDE 10

k = 4

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SLIDE 11

Measure Change in Allegiance

DA(i,k) = Ai,k − Ai,k−1 for k > 1 At k = 1 DA(i,1) = Ai,1 Out degree of actor i

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SLIDE 12

Plot of Change in Allegiance

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SLIDE 13

Sum of Allegiance Change

SDAk = n

i=1 DA(i,k)

Used to estimate k : the number of partitions

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SLIDE 14

Plot of SDAk

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SLIDE 15

Real Example

5 users Oct 2002 - Feb 2004 3000 total servers accessed over 14 months 31 total clients 19 LAN computers

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SLIDE 16

Equivalence Cluster

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SLIDE 17

Individual allegiance Change

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SLIDE 18

Total Allegiance Change

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SLIDE 19

k = 4

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SLIDE 20

k = 5

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SLIDE 21

k = 6

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SLIDE 22

k = 7

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SLIDE 23

k = 8

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SLIDE 24

Conclusions

Allegiance Can be used to estimate number of partitions Used to estimate maximum number of partitions at a minimum Gives a measure for block strength change as partition size changes

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