In765 Knowledge Networks: A Structural Study of Networks Judith Molka-Danielsen Molde University College

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

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.

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)

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

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

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%

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

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

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  …

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

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.

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

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

Unique co-author link distribution – researchers represented individually

Unique Co-Authors versus Publications

Average # of Co-Authors versus Publications

Informatics Institute Cluster: researchers and co-author links

Health Institute Cluster: researchers and co-author links

Social Sciences Institute: researchers and co-author links

Economics/Logistics Cluster: researchers and co-author links

Economics Institute Cluster: researchers and co-author links

Connected Network Tree of researchers and co-author links

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).