New%20York%20Times

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New York Times
Slides thanks to A-L Barabasi
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(Internet?) Big Ideas (3)

• Structure in complex networks

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Erdös-Rényi model (1960)
Pál Erdös (1913-1996)
- Democratic - Random
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Small Worlds

• Stanley Milgram s experiment
• Small Worlds by Watts/Strogatz
• ?(v) Clustering coefficient of node v
• Percentage of neighbours of v
  connected to each other
• Clustering coefficient

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Cluster Coefficient
Clustering My friends will likely know each
other!
Probability to be connected C p
of links between 1,2,n neighbors
C
n(n-1)/2
Networks are clustered large C(p)
but have a small characteristic path
length small L(p).
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Watts-Strogatz Model
C(p) clustering coeff. L(p) average
path length
(Watts and Strogatz, Nature 393, 440 (1998))
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Web
What did we expect?
?k? 6 P(k500) 10-99
NWWW 109 ? N(k500)10-90
We find
?out 2.45
? in 2.1
P(k500) 10-6
NWWW 109 ? N(k500) 103
Pout(k) k-?out
Pin(k) k- ?in
J. Kleinberg, et. al, Proceedings of the ICCC
(1999)
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19 degrees
19 degrees of separation
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l152 1?2?5 l174 1?3?4?6 ? 7 lt l gt ??
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1
4
7
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2
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Power-law Distributions

• Gnutella Node connectivity follows a powerlaw,
  i.e. P(k neighbours) ? k -?

Mapping the Gnutella network Properties of
largescale peer-to-peer systems and implications
for system design. M. Ripeanu, A. Iamnitchi, and
I. Foster. IEEE Internet Computing Journal 6, 1
(2002), 50-57.
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Airlines
What does it mean?
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Internet
INTERNET BACKBONE
Nodes computers, routers Links physical lines
(Faloutsos, Faloutsos and Faloutsos, 1999)
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Internet-Map
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Actors
ACTOR CONNECTIVITIES
Nodes actors Links cast jointly
Days of Thunder (1990) Far and Away (1992)
Eyes Wide Shut (1999)
N 212,250 actors ?k? 28.78
P(k) k-?
?2.3
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Citation
SCIENCE CITATION INDEX
Nodes papers Links citations
Witten-Sander PRL 1981
1736 PRL papers (1988)
P(k) k-?
(? 3)
(S. Redner, 1998)
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Coauthorship
SCIENCE COAUTHORSHIP
Nodes scientist (authors) Links write paper
together
(Newman, 2000, H. Jeong et al 2001)
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Food Web
Nodes trophic species Links trophic
interactions
R.J. Williams, N.D. Martinez Nature (2000)
R. Sole (cond-mat/0011195)
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Most real world networks have the same internal
structure
Scale-free networks
Why?
What does it mean?
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SCALE-FREE NETWORKS
(1) The number of nodes (N) is NOT fixed.
Networks continuously expand by the addition of
new nodes
Examples
WWW addition of new documents
Citation publication of new papers
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BA model
Scale-free model
(1) GROWTH
At every timestep we
add a new node with m edges (connected to the
nodes already present in the system). (2)
PREFERENTIAL ATTACHMENT
The probability ? that a new node will be
connected to node i depends on the connectivity
ki of that node
A.-L.Barabási, R. Albert, Science 286, 509 (1999)
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Achilles Heel
Achilles Heel of complex network
failure
attack
Internet
Protein network
R. Albert, H. Jeong, A.L. Barabasi, Nature 406
378 (2000)
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What Does the Web Really Look Like?

• Graph Structure in the Web, Broder et al.
• Analysis of 2 Altavista crawls, each with over
  200M pages and 1.5 billion links

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Confirm Power Law Structure
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But Things Are More Complex Than One Might Think
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(No Transcript)
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Reading

• Emergence of scaling in random networks,
  Albert-László Barabási, Réka Albert, Science 286
  509-512 (1999)
• Search in power-law networks, Lada A. Adamic,
  Rajan M. Lukose, Amit R. Puniyani and Bernardo A.
  Huberman, Phys. Rev. E, 64 46135 (2001)
• Graph structure in the web, Andrei Broder, Ravi
  Kumar, Farzin Maghoul, Prabhakar Raghavan,
  Sridhar Rajagopalan, Raymie Stata, Andrew
  Tomkins, Janet Wiener, Comput. Netw. 33 309

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CMSC 23340-1 (Winter 2005)Course Goals

• Primary
• Gain deep understanding of fundamental issues
  that effect design of large-scale networked
  systems
• Map primary contemporary research themes
• Gain experience in network research
• Secondary
• By studying a set of outstanding papers, build
  knowledge of how to present research
• Learn how to read papers evaluate ideas

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How the Class Works

• Research papers
• Prior to each class, we all read and evaluate two
  research papers
• During each class, we discuss those papers
• Project