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/
WeST
Steffen Staab
[email protected]
1
Network Type
By content
 Information network
(example?)
 Communication network
(example?)
 Social network
(example?)
 Further examples
WeST
Steffen Staab
[email protected]
2
…traditional social networks
Florentine
marriages
in 1400
WeST
Steffen Staab
[email protected]
3
Beyond the web
…traditional social networks
Florentine
marriages
in 1400
(from Leeat Yariv)
WeST
Steffen Staab
[email protected]
4
…transportation networks
Tokyo metro
European airlines
WeST
Steffen Staab
[email protected]
5
…coauthor & citation networks
Citations among
biochem patents
WeST
Steffen Staab
[email protected]
6
…biological networks
Biochemical
pathways of
malaria
WeST
Steffen Staab
[email protected]
7
Network Type
By content
By structure
 Information network
(example?)
 Communication network
(example?)
 Social network
(example?)
 Further examples





WeST
Steffen Staab
[email protected]
8
Directed
Undirected
Weighted
Signed
Bipartite
Two example toy social networks
WeST
Steffen Staab
[email protected]
9
Questions to ask
What makes the two
different? How to
measure this?
WeST
Steffen Staab
[email protected]
10
Questions to ask
What is the best
position to be in?
WeST
Steffen Staab
[email protected]
11
Questions to ask
How long does it for
information to travel?
WeST
Steffen Staab
[email protected]
12
Questions to ask
Which new link to
suggest?
WeST
Steffen Staab
[email protected]
13
SMALL WORLD PHENOMENA
WeST
Steffen Staab
[email protected]
14
How many friends do people have on Facebook?
Lars Backstrom, 22. November 2011
https://www.facebook.com/notes/facebook-datateam/anatomy-of-facebook/10150388519243859
 721 million active Facebook users
(more than 10% of the global population)
 69 billion friendships between them
WeST
Steffen Staab
[email protected]
15
How many friends do people have on Facebook?
Cumulative degree distribution
Median: ~100
Average: ~190
WeST
What is the implication?
Steffen Staab
[email protected]
16
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
 …
WeST
Steffen Staab
[email protected]
17
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.
WeST
Steffen Staab
[email protected]
18
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
WeST
Steffen Staab
[email protected]
19
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….
WeST
Steffen Staab
[email protected]
20