COLOR TEST COLOR TEST. Social Networks: Structure and Impact N ICOLE I MMORLICA, N ORTHWESTERN U.
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Transcript of COLOR TEST COLOR TEST. Social Networks: Structure and Impact N ICOLE I MMORLICA, N ORTHWESTERN U.
![Page 1: COLOR TEST COLOR TEST. Social Networks: Structure and Impact N ICOLE I MMORLICA, N ORTHWESTERN U.](https://reader036.fdocuments.in/reader036/viewer/2022062719/56649ed05503460f94bddcc1/html5/thumbnails/1.jpg)
COLOR TESTCOLOR TESTCOLOR TESTCOLOR TEST
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Social Networks:Structure and Impact
NICOLE IMMORLICA, NORTHWESTERN U.
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Graph Representation
Nodes: =
Edges: =
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New Testament
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Visualization from ManyEyes
New Testament
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Scientific Collaboration
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Scientific Collaboration
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World Wide Web
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World Wide Web
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Seattle
Honolulu
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thesis:
networks are basic structure upon which society operates
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spread of disease.
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diffusion of ideas.
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models of social networks
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A theory must be tempered with reality.
– Jawaharlal Nehru, Indian Prime Minister
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which is the best theory?
grid star cycle “tree”
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“reality”:
1. power-law degree dist.Popular people are really
popular. Most people aren’t.
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1
7
Degrees
2
8
3
4
5
6
Definition: The degree of a node vi is the number of nodes vj such that there’s an edge ei,j between them.
Degree v8 = 4.
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Degree Distributions
0 1 2 3 4
0
1/4
1/2
3/4
5 6 7 8
1
Frequency
# of friend (degree)
A cycle?
Cycle deg. dist.
A star?
Star deg. dist.
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Power-law Degree Dist.
0 1 2 3 4
0
1/3
1/2
5 6 7 8
1
Frequency
Degree
Power-law: P(∂) = c∂-α
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Log-Log PlotsLog (Frequency)
Log (Degree)
Power-law: P(∂) = c∂-α
log (P(∂)) = log (c∂-α)= log (c) – α∙log (∂)
Straight line on a log-log plot!
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Example: Web Graph In-Degree
Power law exponent: α = 2.09
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Example: New York Facebook
Lognormal is better fit.
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“reality”:
2. small diameterMost people know people who know people who know people who … know Obama.
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Paths
1
2
8
3
7
4
5
6
Definition: A path is a sequence of nodes (v1, …, vk) such that for any adjacent pair vi and vi+1, there’s an edge ei,i+1 between them.
Path (v1,v2,v8,v3,v7)
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Paths
“I know someone who knows someone who knows you.”
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Path length
Definition: The length of a path is the number of edges it contains.
Path (v1,v2,v8,v3,v7)has length 4.
1
2
8
3
7
4
5
6
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Distance
Definition: The distance between nodes vi and vj is the length of the shortest path connecting them.
The distance between v1 and v7 is 3.
1
2
8
3
7
4
5
6
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Famous distances
nodes = {mathematicians}edges = if 2 mathematicians co-author a paper
Erdos number = distance between mathematican and Erdos
Paul Erdos number
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Famous distances
Erdos number of …
http://www.oakland.edu/enp/
= 4
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Diameter
Definition: The diameter of a graph is the maximum shortest-path distance between any two nodes.
The diameter is 3.
1
2
8
3
7
4
5
6
“longest shortest path”
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The trace of a disease
1. Initially just one node is infected2. All nodes with an infected friend get infected
Day 0Day 1Day 2
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The trace of a disease
# days ≤ diameter ≤ twice # days
Day 0Day 1Day 2
Because the trace defines the distance from the initially infected person to the last infected person.
Because there’s a path in the trace between any two people going through the initially infected person.
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Six degrees of separation
The diameter of a social network is typically small.
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Small world phenomenon
Milgram’s experiment (1960s).
Ask someone to pass a letter to another person via friends knowing only the name, address, and occupation of the target.
Short paths exist (and people can find them!).
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Diameter
“longest shortest path”
grid star tree
√n 2 log n(for const. deg.)
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Diameter
For the population of the US,
grid star tree
2,000 2 6
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“reality”:
3. high clusteringMost people’s friends are
themselves friends.
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Clustering Coefficient
“fraction of triangles bt. all connected triples”
ZERO …. > ZERO
grid star cycle “tree”
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Why do we see these realities?
1. High clustering coefficient… triadic closure – tend to know your friend’s friends
2. Power-law degree distribution… popular people attract proportionally more friends
3. Low diameter… there is an element of chance to whom we meet
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preferential attachment:
People are imitators. They make the choices their
friends make.
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Preferential Attachment
1. People join network in order 1, 2, …, N2. When join, person t chooses friend by
a) With probability p, pick person t’ uniformly at random from 1, …, t-1
b) With probability (1-p), pick person t’ uniformly at random and link to person that t’ links too
Imitation
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The rich get richer
2 b) With prob. (1-p), pick person t’ uniformly at random and link to person that t’ links too
1/43/4
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The rich get richer
2 b) With prob. (1-p), pick person t’ uniformly at random and link to person that t’ links too
Equivalently,
2 b) With probability (1-p), pick a personproportional to in-degree and link to him
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preferential attachment:
The degree distribution follows a power-law.
– Albert-L szl Barabasi and R ka Albert (1999): a� o̒� e�Emergence of Scaling in Random Networks, Science
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can we use network structure to explain success of various technologies/fads/rumors?
impact of social networks
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1. spread technology.impact of social networks
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key: = Instant Msg A user= Instant Msg B user
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f ( new ) > f ( old )
… if enough friends use !
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1. relative quality: f ( new ) >> f ( old )
How can we convincepeople to use ?
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1. relative quality, 2. compatibility:
How can we convincepeople to use ?
= user of both technologies
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Lessons [IKMW’05].
1. Inferior incumbents can always survive invasion of slightly superior competitors by adopting limited levels of compatibility.
2. This happens through the formation of bi-lingual buffers.
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2. generate revenue.impact of social networks
$10$0
$11
$8
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Lesson [HIMM’11].
When selling a socially-enabled product in a social network, must subsidize influential nodes.
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3. encourage cooperationimpact of social networks
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nice guys have more friends
Lesson [ILR’10].
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Conclusion
• Social networks have predictable structure– Power-law degree distribution
(preferential attachment model)– Low (logarithmic) diameter– High clustering coefficients
• Social networks impact many social processes– Spread disease/technology– Generate revenue– Sustain cooperation