2. © 2006 Board of Trustees of the University of Illinois Authored by Tanya Berger-Wolf Analysis of Dynamic Social Networks Tanya Berger-Wolf Department of Computer Science University of Illinois at Chicago Tanya Berger-Wolf Department of Computer Science University of Illinois at Chicago

3. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Zebras Dan Rubenstein, Siva Sandaresan, Ilya Fischhoff (Princeton) Movie credit: “Champions of the Wild”, © Omni-Film Productions.

4. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Context disease modeling Eubank et.al.‘04, Keeling’99, Kretzschmar&Morris’96 cultural and information transmission Baumes et.al.’04, Broido&Claffy’01, Carley’96, Chen&Carley’05, Kempe et.al.’03, Tsvetovat et.al.’03,Tyler et.al.’03, Wellman’97 intelligence and surveillance Airoldi&Malin’04,Baumes et.al.’04, Kolata’05, Malin’04, Magdon-Ismail et.al.’03 business management Bernstein et.al.’02, Carley&Prietula’01, Papadimitriou’97, Papadimitriou&Servan-Schreiber’99 conservation and population biology Croft et.al.’04, Cross et.al.’05, Lusseau&Newman’04 disease modeling Eubank et.al.‘04, Keeling’99, Kretzschmar&Morris’96 cultural and information transmission Baumes et.al.’04, Broido&Claffy’01, Carley’96, Chen&Carley’05, Kempe et.al.’03, Tsvetovat et.al.’03,Tyler et.al.’03, Wellman’97 intelligence and surveillance Airoldi&Malin’04,Baumes et.al.’04, Kolata’05, Malin’04, Magdon-Ismail et.al.’03 business management Bernstein et.al.’02, Carley&Prietula’01, Papadimitriou’97, Papadimitriou&Servan-Schreiber’99 conservation and population biology Croft et.al.’04, Cross et.al.’05, Lusseau&Newman’04

5. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Social Networks: Static vs Dynamic 123456123456 t=1t=2t=3t=4 t=5 1 2 3 4 5 6 123456123456 123456123456 1/5 Individuals Strength or probability of interaction over a period of time

6. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Input – Individual Information 2 1 3456

7. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf file 4 9 3 1 1 © Christopher Sadler

8. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf 4 9 3 1 1 t=1 4 8 3 2 2 1 t=2 9 4 4 4 9 1 t=4 4 4 4 8 2 2 t=3

9. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Communities over time – persistent groups Critical individuals (starters and blockers) Critical gatherings Critical times Persistent demographic configurations Communities over time – persistent groups Critical individuals (starters and blockers) Critical gatherings Critical times Persistent demographic configurations Communities over time – persistent groups A group persist in time (is a metagroup) if some (big) fraction β of it exists some (big) fraction α of time Critical individuals (starters and blockers) Critical starter = a spreading process started with it will affect most individuals. Critical blocker = a spreading process will affect fewest individuals with it absent from the population. Critical gatherings Gatherings that facilitate most (least) spreading Critical times Timesteps when interaction pattern changes Persistent demographic configurations Repeated groups with the same demographic pattern Communities over time – persistent groups A group persist in time (is a metagroup) if some (big) fraction β of it exists some (big) fraction α of time Critical individuals (starters and blockers) Critical starter = a spreading process started with it will affect most individuals. Critical blocker = a spreading process will affect fewest individuals with it absent from the population. Critical gatherings Gatherings that facilitate most (least) spreading Critical times Timesteps when interaction pattern changes Persistent demographic configurations Repeated groups with the same demographic pattern Questions

10. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf 1/10 1/9 1/4 1 4 9 3 1 1 t=1 4 8 3 2 2 1 t=2 9 4 4 4 9 1 t=4 4 4 4 8 2 2 t=3 111 8/9 1 1 1 1 1 3/4 1/2 β=.5β=.8

11. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Simple Stats: Metagroup = path length ≥ α Total #metagroups = #paths length ≥ α Maximal metagroup length = max path length Most persistent metagroup = longest path in a DAG Let x be a member of MG is it appears in it at least γ times. Largest metagroup = dynamic programming on membership set. Metagroup = path length ≥ α Total #metagroups = #paths length ≥ α Maximal metagroup length = max path length Most persistent metagroup = longest path in a DAG Let x be a member of MG is it appears in it at least γ times. Largest metagroup = dynamic programming on membership set. Skip 3 Skip 3 Skip 5 Skip 5

12. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Example – Southern Women (Natches, TN 1933) A. Davis, B. B. Gardner, and M. R. Gardner. Deep South. The U. of Chicago Press, Chicago, IL, 1941

13. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Southern Women Metagroups 1152712936101148413.61-.7.71-.8.81-.9.91-1 10 11 12 13 14 15 11 12 13 14 15 12 13 14 12 13 14 1234567912345679 123456123456 12346781234678 13451345

14. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf DGG1941Intuition Homans 1951Intuition Phillips and Conviser 1972Information Theory Breiger 1974Matrix Algebra Breiger, Boorman & Arabie 1975Computational Bonacich 1978Boolean Algebra Doreian 1979Algebraic Topology Bonacich 1991Correspondence Analysis Freeman1992G-Transitivity Everett & Borgatti1993Regular Coloring Freeman1993Genetic Algorithm I & II Freeman & White1993Galois Lattices I & II Borgatti & Everett 1997Bipartite Analyses I, II & III Skvoretz & Faust1999p* Model Roberts2000Normalized SVD Osbourn2000VERI Procedure Newman2001Weighted Proximities Linton Freeman Metanalysis, 2003

15. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Southern Women Communities

16. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Southern Women: Core vs Periphery BW&S1 3 4 5 | 2 6 | 7 912 13 14 | 11 15 | 10

17. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Group Connectivity Given groups g 1,…,g l, are they in the same metagroup? Most persistent/largest/loudest/.. metagroup that contains these groups A metagroup that contains largest number of these groups – dynamic programming … g1g1 g2g2 g l-1 glgl

18. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Individual Connectivity Given individuals S={s 1,…,s l }, are they in the same metagroup? Metagroup that contains max number of individuals in S Most persistent/largest/shiniest.. metagroup that contains all individuals in S Given individuals S={s 1,…,s l }, are they in the same metagroup? Metagroup that contains max number of individuals in S Most persistent/largest/shiniest.. metagroup that contains all individuals in S

19. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Critical Group Set The smallest set of groups whose absence leaves no metagroups (for given α and β) Formally: remove fewest vertices in a DAG so there are no paths of length > k-1 K-path Vertex Shattering Set

20. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf K-path Vertex Shattering Set NP-hard: 2-path shattering set = vertex cover k=2 k=T ? Polynomial: T-path shattering set (T is the longest path length) – min vertex cut in a DAG

21. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Critical Individual Set The smallest set of individuals whose absence leaves no metagroups (for given α and β) c d c d c d … cd cd a a a aaabbb b b b cd

22. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Other questions: Close Group: individuals that appear together more than others. Loyal Individuals: appear most frequently in any metagroup. Individual Membership: metagroup which maximizes the cardinality of the set of groups in which a given individual occurs. Extra/Introvert: member of the largest/smallest number of metagroups. Metagroup Representative: an individual who occurs more in a metagroup than any other individual and occurs in it more than in any other metagroup. Demographic Distinction: given a coloring of individuals, is there a property that distinguishes one color from the others? Critical Parameter Values: largest values of α, β for which there exists at least k metagroups. Largest γ for which each metagroup has at least k members. Sampling Rate: largest time step such that the answer does not change if the time step is decreased but changes if it is increased. Critical Time Moments: e.g., the time when the groups' membership changes most, i.e. minimal edge weight sum between time steps. Data Augmented Solution Reconciliation: given partial sets of observations and a partial solution, find is the combined solution to the entire input. Close Group: individuals that appear together more than others. Loyal Individuals: appear most frequently in any metagroup. Individual Membership: metagroup which maximizes the cardinality of the set of groups in which a given individual occurs. Extra/Introvert: member of the largest/smallest number of metagroups. Metagroup Representative: an individual who occurs more in a metagroup than any other individual and occurs in it more than in any other metagroup. Demographic Distinction: given a coloring of individuals, is there a property that distinguishes one color from the others? Critical Parameter Values: largest values of α, β for which there exists at least k metagroups. Largest γ for which each metagroup has at least k members. Sampling Rate: largest time step such that the answer does not change if the time step is decreased but changes if it is increased. Critical Time Moments: e.g., the time when the groups' membership changes most, i.e. minimal edge weight sum between time steps. Data Augmented Solution Reconciliation: given partial sets of observations and a partial solution, find is the combined solution to the entire input.

23. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Conclusions New data structure with explicit time component of social interactions Generic – applicable in many contexts Powerful – can ask meaningful questions (finding leaders of zebras) But! (And?) many hard questions – lots of work! New data structure with explicit time component of social interactions Generic – applicable in many contexts Powerful – can ask meaningful questions (finding leaders of zebras) But! (And?) many hard questions – lots of work!

24. © 2006 Board of Trustees of the University of Illinois. Authored by Tanya Berger-Wolf Credits: Jared Saia (UNM) Dan Rubenstein (Princeton) Siva Sundaresan Ilya Fischoff Simon Levin (Princeton) S. Muthu Muthukrishnan (Rutgers) David Kempe (USC) Habiba Habiba (UIC) Mayank Lahiri (UIC) Chayant Tantipasanandth (UIC) Microsoft NSF

25. © 2006 Board of Trustees of the University of Illinois Authored by Tanya Berger-Wolf © 2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.