1. In765 Knowledge Networks: A Structural Study of Networks Judith Molka-Danielsen Molde University College j.molka-danielsen@himolde.no http://home.himolde.no/~molka 2005

2. Types of Networks.. Social Networks Friends, families, colleagues Logical Resources web-pages,P2P-Gnutella Telephone Wireline, mobile Transport Roads, railroads, airline, electricity Economic Firms, markets, organization Physical Resources Internet IP routers

3. Why Study Networks? Research Areas  Availability and vulnerability of services: electric, telephone, air connections, etc.  Preventing or stopping of viruses on data networks.  The importance of weak ties: connectivness to the core, finding a job, finding a web page.  The characterization of network structure and the role of hubs in the spreading an idea, or proliferation of a product, and managing organizations.

4. Former Research  Random Network Theory –Erdös & Rényi (1960)  Six Degrees of Separation –S.Milgram (1967)  Cluster Coefficient –Small Worlds – Watts & Strogatz (1998)  Hubs and Scale Free Networks – Albert, Jeong, & Barab á si (1999)  Hubs in Social Networks – Malcolm Gladwell (2000)

5. Random Networks Erdös-Rényi model (1960) - Democratic - Random Pál Erdös (1913-1996) Connect with probability p p=1/6 N=10  k  ~ 1.5 Poisson distribution

6. Six Degrees of Separation Nodes: individuals Links: social relationship (family/work/friendship/etc.) S. Milgram (1967) Social networks: Many individuals with diverse social interactions between them. John Guare (1980) Six Degrees of Separation

7. Cluster Coefficient Clustering: My friends will likely know each other! Probability to be connected C » p C = # of links between 1,2,…n neighbors n(n-1)/2 C friends = 15/ [6(5)/2] = 100%

8. Hubs in Networks  200 million searches each day  More than 2300 searches per second  In 88 languages  3.2 billion web pages indexed.  10 000 super computers perform the searches.

9. Do we find Hubs in Social Networks? Yes.  Most influencial  Access to the most information  Impacts others decisions most  Have the most power

10. Who do you know? (similar to a study by Malcolm Gladwell, 2000)  Bjørnstjerne Bjørnsons Vei  Alme Jørund  Andenes Aud  Andestad Reidar  Bakke Gerd Inger  Bergseth Egil  Bergtun Lill Eldrid  Bjøringsøy Karl Magnar  Bjørkly Jorunn  Bjørkly Åsa Bjordal  Bjørnebo Solveig Randi Midtbø  Broks Vivi-Annie  Brokstad Jon  Drageseth Dagfinn  Dyrli Janne Merete  Døving Ellen  Eilertsen Gudny  Flø Jorunn Marie  Fylling Lars Kristen Tovan  Gjære Arne  Gjære Guro Wiersholm  Gjære Vibeke Wiersholm  Grønbugt Rutt  Grønset Erling Rune  Gudbrandsen Åste Einbu  Gøncz Geir Janos  Göncz Arne  Hansen Helge  Hansen Sissel  Helde Marit Illøkken  Henriksen Line  Hjelmsøt Maria  Hoem Jermund  Hofset Siv  Jenset Grete  Jenset Torbjørn  Jordet Birgit  Kanestrøm Andreas Julshamn  …

11. 12- 15 1 8-113 4-75 0-313 151101 91 81 62 52 31 24 16 03 A = number of persons known on the list. B = number of persons (nodes) that person A knows. AB AB Who do you know?: survey to faculty gruppert 22

12. 15- 23 1 7-141 5-62 2-48 0-136 231141 61 51 44 31 23 116 020 AB AB Who do you know?: survey to students gruppert 48 A = number of persons known on the list. B = number of persons (nodes) that person A knows.

13. Scale Free Networks and Power Laws by Albert, Jeong, Barabasi.

14. Collaboration Among Researchers Networks have diverse nodes and links are -computers -routers -satellites - researchers -phone lines -TV cables -EM waves - co-authorship

15. Unique co-author link distribution – researchers represented individually

16. Unique Co-Authors versus Publications

17. Average # of Co-Authors versus Publications

18. Informatics Institute Cluster: researchers and co-author links

19. Health Institute Cluster: researchers and co-author links

20. Social Sciences Institute: researchers and co-author links

21. Economics/Logistics Cluster: researchers and co-author links

22. Economics Institute Cluster: researchers and co-author links

23. Connected Network Tree of researchers and co-author links

24. Conclusions  Network of researchers at HSM is a Scale Free network. (existance of hubs, clustering coeffiencient)  Co-authors are not chosen randomly.  Co-authorship & Publication count: (cannot claim causality) –Average # of co-author per paper is the same regardless of the total # of publications per author. (does not help) –Average # of unique associations is related to a total # of publications per author. (helps)  Role of “ connectors” (nodes with a high # of external links) are important –They often have high publication counts. –They have more external contacts. –They are more likely to hold a joint appointment (again not causal).