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Network Theory and Dynamic Systems Networks – Part 2

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/. Network Type. By content Information network ( example ?) Communication network ( example ?)

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Network Theory and Dynamic Systems Networks – Part 2

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  1. Network Theory and Dynamic SystemsNetworks – Part 2 Prof. Dr. Steffen Staab Dr. Christoph Ringelstein AcknowledgementstoAdam Wierman et al, http://courses.cms.caltech.edu/cs144/

  2. Network Type Bycontent • Information network (example?) • Communication network (example?) • Socialnetwork (example?) • Further examples

  3. Beyond the web …traditional social networks Florentinemarriagesin 1400

  4. Beyond the web …traditional social networks Florentinemarriagesin 1400 (from LeeatYariv)

  5. Beyond the web …transportation networks Tokyo metro European airlines

  6. Beyond the web …coauthor & citation networks Citations amongbiochem patents

  7. Beyond the web …biological networks Biochemical pathways ofmalaria

  8. Network Type Bycontent • Information network (example?) • Communication network (example?) • Socialnetwork (example?) • Further examples Bystructure • Directed • Undirected • Weighted • Signed • Bipartite

  9. Twoexampletoysocialnetworks

  10. Questionstoask Whatmakesthetwo different? Howtomeasurethis?

  11. Questionstoask Whatisthebestpositiontobe in?

  12. Questionstoask Howlongdoesitforinformationtotravel?

  13. Questionstoask Whichnew link tosuggest?

  14. Small World Phenomena

  15. Howmanyfriends do peoplehave 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. Howmanyfriends do peoplehave on Facebook? Cumulativedegreedistribution Median: ~100 Average: ~190 Whatistheimplication?

  17. Howmanyfriends do peoplehave on Facebook? Seeming paradox impliedbytheskew: • Most ofyourfriendshavemorefriendsthanyouhave • Most oftheflightsyouare in arecrowded • Most ofthe time (but not mostofthetimes!) yourlineatthecountermovestheslowest • …

  18. Howfararethesefriendsaway? • 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. Confirmed in manystudies • Microsoft Instant Messenger (240 millionactiveusers) • Erdösnumber: Distanceto Paul Erdös(whohad 1500 publications) • Bacon number: Kevin Bacon • Biggestnumber in IMDB(www.imdb.de/) is 8 for a Soviet film from 1929

  20. Summary • Therearenetworksofmanycontenttypes • Therearenetworksofmany link types • Therearefurthercharacteristicslike: • (In-/out-)Degreedistributionofnodes • Average and median distance • Andmorecomingup….

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