1. Steffen Staab staab@uni-koblenz.de 1WeST Web Science & Technologies University of Koblenz ▪ Landau, Germany Network Theory and Dynamic Systems Networks – Part 2 Prof. Dr. Steffen Staab Dr. Christoph Ringelstein Acknowledgements to Adam Wierman et al, http://courses.cms.caltech.edu/cs144/

2. Steffen Staab staab@uni-koblenz.de 2WeST Network Type By content  Information network (example?)  Communication network (example?)  Social network (example?)  Further examples

3. Steffen Staab staab@uni-koblenz.de 3WeST Beyond the web …traditional social networks Florentine marriages in 1400

4. Steffen Staab staab@uni-koblenz.de 4WeST Beyond the web …traditional social networks Florentine marriages in 1400 (from Leeat Yariv)

5. Steffen Staab staab@uni-koblenz.de 5WeST Beyond the web …transportation networks Tokyo metro European airlines

6. Steffen Staab staab@uni-koblenz.de 6WeST Beyond the web …coauthor & citation networks Citations among biochem patents

7. Steffen Staab staab@uni-koblenz.de 7WeST Beyond the web …biological networks Biochemical pathways of malaria

8. Steffen Staab staab@uni-koblenz.de 8WeST Network Type By content  Information network (example?)  Communication network (example?)  Social network (example?)  Further examples By structure  Directed  Undirected  Weighted  Signed  Bipartite

9. Steffen Staab staab@uni-koblenz.de 9WeST Two example toy social networks

10. Steffen Staab staab@uni-koblenz.de 10WeST Questions to ask What makes the two different? How to measure this?

11. Steffen Staab staab@uni-koblenz.de 11WeST Questions to ask What is the best position to be in? (Macy, Science 2011)

12. Steffen Staab staab@uni-koblenz.de 12WeST Questions to ask How long does it for information to travel?

13. Steffen Staab staab@uni-koblenz.de 13WeST Questions to ask Which new link to suggest?

14. Steffen Staab staab@uni-koblenz.de 14WeST SMALL WORLD PHENOMENA

15. Steffen Staab staab@uni-koblenz.de 15WeST How many friends do people have on Facebook? Lars Backstrom, 22. November 2011 https://www.facebook.com/notes/facebook-data- team/anatomy-of-facebook/10150388519243859  721 million active Facebook users (more than 10% of the global population)  69 billion friendships between them

16. Steffen Staab staab@uni-koblenz.de 16WeST How many friends do people have on Facebook? Cumulative degree distribution Median: ~100 Average: ~190 What is the implication?

17. Steffen Staab staab@uni-koblenz.de 17WeST How many friends do people have on Facebook? Seeming paradox implied by the skew:  Most of your friends have more friends than you have  Most of the flights you are in are crowded  Most of the time (but not most of the times!) your line at the counter moves the slowest  …

18. Steffen Staab staab@uni-koblenz.de 18WeST How far are these friends away?  99.6% of all pairs of users are connected by paths with 5 degrees (6 hops),  92% are connected by only four degrees (5 hops).  The average distance in 2011 was 4.74.

19. Steffen Staab staab@uni-koblenz.de 19WeST Confirmed in many studies  Microsoft Instant Messenger (240 million active users)  Erdös number: Distance to Paul Erdös (who had 1500 publications)  Bacon number: Kevin Bacon  Biggest number in IMDB (www.imdb.de/) is 8 for a Soviet film from 1929

20. Steffen Staab staab@uni-koblenz.de 20WeST Summary  There are networks of many content types  There are networks of many link types  There are further characteristics like:  (In-/out-)Degree distribution of nodes  Average and median distance  And more coming up….