Steffen Staab 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,

Steffen Staab 2WeST Network Type By content  Information network (example?)  Communication network (example?)  Social network (example?)  Further examples

Steffen Staab 3WeST Beyond the web …traditional social networks Florentine marriages in 1400

Steffen Staab 4WeST Beyond the web …traditional social networks Florentine marriages in 1400 (from Leeat Yariv)

Steffen Staab 5WeST Beyond the web …transportation networks Tokyo metro European airlines

Steffen Staab 6WeST Beyond the web …coauthor & citation networks Citations among biochem patents

Steffen Staab 7WeST Beyond the web …biological networks Biochemical pathways of malaria

Steffen Staab 8WeST Network Type By content  Information network (example?)  Communication network (example?)  Social network (example?)  Further examples By structure  Directed  Undirected  Weighted  Signed  Bipartite

Steffen Staab 9WeST Two example toy social networks

Steffen Staab 10WeST Questions to ask What makes the two different? How to measure this?

Steffen Staab 11WeST Questions to ask What is the best position to be in? (Macy, Science 2011)

Steffen Staab 12WeST Questions to ask How long does it for information to travel?

Steffen Staab 13WeST Questions to ask Which new link to suggest?

Steffen Staab 14WeST SMALL WORLD PHENOMENA

Steffen Staab 15WeST How many friends do people have on Facebook? Lars Backstrom, 22. November team/anatomy-of-facebook/  721 million active Facebook users (more than 10% of the global population)  69 billion friendships between them

Steffen Staab 16WeST How many friends do people have on Facebook? Cumulative degree distribution Median: ~100 Average: ~190 What is the implication?

Steffen Staab 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  …

Steffen Staab 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.

Steffen Staab 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 ( is 8 for a Soviet film from 1929

Steffen Staab 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….