Презентация Леонида Жукова: От микромотивов до макроповедения

Social Networks:
from Micromotives to
Macrobehavior
Leonid Zhukov

Moscow, June 2014

http://bks5.books.google.ru/books?
id=AOsWGCuRDhkC&printsec=frontcover&img=1&zoom=1&im
gtk=AFLRE71eJXO_WkVQX1OwrD8c5jzrap6PMfFt6GPTfvFv7y
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vvK8lOlA9ZxSCE39_Fr1KvgDuwmCxWJqyMirnJe4Bh4K1NNeE
RlH3ei49yR4inV085FAPrsEl9V763tRfqakMvrJHu
Micromotives and
macrobehavior
Combined local actions -> global results

Simple rules -> complex behavior

Local structure -> global properties
Thomas C. Shelling, 1978!
Nobel Prize in Economics 2005

Talk outline
Network structure

Network models

Processes on networks

Complex networks:
social networks, internet, WWW, citation networks,
ﬁnancial networks, trade networks, transportation
networks, protein interaction networks, brain
networks, food web, language networks, …

Local structure
Node degree = # of friends

Global: degree distribution
How many people with:

1 friend

2 friends

3 friends

!
Distribution: P(n)

Power-law distribution

Local structure
Node degree = # of friends!
Friend’s friends = triangles

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The strength of weak
“The Strength of Weak Ties”. Mark Granovetter. 1973
Mark Granovetter. The strengtth of weak ties , American Journal of Sociology, 78(6):1360-1380, 1973

Triadic closer
Strength of ties

Triadic closure: if A and B
and A and C are strongly
linked, then the tie between
B and C is always present

Clustering coeﬃcient

Local structure
Node degree = # of friends!
Friend’s friends = triangles!
“Long connections” = small
network diameter

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Small world
J. Travers and S. Milgram. An Experimental Study of the Small World Problem. Sociometry, vol 32, No 4, pp 425-433, 1969

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1969 Experiment
296 volunteers, 217 sent

196 Nebraska (1300 miles)

100 Boston (25 miles)

target in Boston
vaguely ‘out there,’ on the Great Plains or somewhere.” There was little
consensus about how many links it would take to connect people from
these remote areas. Milgram himself pointed out in 1969, “Recently I
asked a person of intelligence how many steps he thought it would take,
and he said that it would require 100 intermediate persons, or more, to
move from Nebraska to Sharon.”
Milgram’s experiment entailed sending letters to randomly chosen
residents of Wichita and Omaha asking them to participate in a study
of social contact in American society. The letter contained a short
summary of the study’s purpose, a photograph, and the name and ad-
dress of and other information about one of the target persons, along
with the following four-step instructions:
HOW TO TAKE PART IN THIS STUDY
1. ADD YOUR NAME TO THE ROSTER AT THE BOT-
TOM OF THIS SHEET, so that the next person who re-
ceives this letter will know who it came from.
2. DETACH ONE POSTCARD. FILL IT OUT AND RE-
TURN IT TO HARVARD UNIVERSITY. No stamp is
needed. The postcard is very important. It allows us to keep
track of the progress of the folder as it moves toward the tar-
get person.
3. IF YOU KNOW THE TARGET PERSON ON A PER-
SONAL BASIS, MAIL THIS FOLDER DIRECTLY TO
HIM (HER). Do this only if you have previously met the
target person and know each other on a first name basis.
4. IF YOU DO NOT KNOW THE TARGET PERSON ON A
PERSONAL BASIS, DO NOT TRY TO CONTACT HIM
DIRECTLY. INSTEAD, MAIL THIS FOLDER (POST-
CARDS AND ALL) TO A PERSONAL ACQUAIN-
TANCE WHO IS MORE LIKELY THAN YOU TO
KNOW THE TARGET PERSON. You may send the folder
to a friend, relative or acquaintance, but it must be someone
you know on a first name basis.
Milgram had a pressing concern: Would any of the letters make it
to the target? If the number of links was indeed around one hundred, as
his friend guessed, then the experiment would likely fail, since there is
always someone along such a long chain who does not cooperate. It was
therefore a pleasant surprise when within a few days the first letter ar-
rived, passing through only two intermediate links! This would turn out
to be the shortest path ever recorded, but eventually 42 of the 160 let-
ters made it back, some requiring close to a dozen intermediates. These
completed chains allowed Milgram to determine the number of people
Six Degrees of Separation 29
0738206679-01.qxd 3/13/02 2:08 PM Page 29
NAME, ADDRESS, OCCUPATION, JOB, HOMETOWN

1969 Experiment
reached the target N = 64, 29%

ave chain length <l> = 5.2

channels:

hometown <l> = 6.1

business contacts <l> = 4.6

Location:

boston <l> = 4.4

nebraska <l> = 5.7

1994,Premiere magazine
Six degrees of
Kevin Bacon

Universal properties of
social networks
Power low degree distribution

Large clustering coeﬃcient

Small world eﬀect

!
Gigantic connected component

Tight core and periphery

Hierarchical structure

Small world
network
Duncan J. Watts and Steven H. Strogatz. Collective dynamics of ‘small-world’ networks. . Nature 393:440-42, 1998.

Preferential attachement
AL Barabasi and R. Albert. Emergence of Scaling in Random Networks. Science, 286, 1999.

Strategic network
formation
Utility function

Distance based utility

Costs and beneﬁts of
connections

Maximizing individual utility
Matthew O. Jackson, Asher Wolinsky, . A Strategic Model of Social and Economic Networks. Journal of Economic Theory, Vol 71, pp 44-74, 1996.
50 CHAPTER 2. REPRESENTING AND MEASURING NETWORKS

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Strategic network
formation
Pairwise stable small world network224 CHAPTER 6. STRATEGIC NETWORK FORMATION
Figure 6.5.1. A Pairwise Stable ìSmall Worldî in an Islands Version of the
Connections Model
The intuition behind the proposition is relatively straightforward. Low costs of
connections to nearby players (those on the same island) lead to high clustering. The

Processes on networks
Information propagation

diﬀusive

virus like

Decision making

threshold models

Diffusion model
method - diﬀusion

virus model

“infected” on contact

probability depends on
immunity

can model

news

gossips

Diffusion model
Step 5
!
Complete coverage

Process time depends
on the source

Based on connectivity
pattern

Twitter
retweet

mention
“Truthy” Project. Center for Complex Networks and System
Research. Indiana University.
#newsjp
#iraq
#ocra

Threshold model
neighbors “opinion”

decision threshold

information cascade

model:

beliefs propagation

purchasing decisions

spread of innovations
A,B - types of behavior

q –decision threshold

If fraction of neighbors with A
greater than q, accpet A

Threshold model
threshold= 1/2

Threshold model
Step 1
2 sources

threshold= 2/5

Threshold model
Step 4
incomplete cascade

depends on network
topology

strongly depends on
source selection

Cascade maximization
Cascade maximization problem

Strategic source placement

Well connected group of nodes

Inside various communities

Increase of competitive advantage

reduce threshold level

Visual Complexity
www.visualcomplexity.com

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Textbooks

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Easy read

Презентация Леонида Жукова: От микромотивов до макроповедения

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Презентация Леонида Жукова: От микромотивов до макроповедения