http://web.yonsei.ac.kr/yoosik/index.htm

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?

The movie shows a journey through the simulated universe. On the way, we visit a rich cluster of galaxies and fly around it. During the two minutes of the movie, we travel a distance for which light would need more than 2.4 billion years.

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Snapshot of the Universe

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Another Universe?

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Same look with a little different size

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August 15, 2006 New York Times

SCIENCE ILLUSTRATED; They Look Alike, but There's a Little Matter of Size

By DAVID CONSTANTINE

One is only micrometers wide. The other is billions of light-years across. One shows neurons in a mouse brain. The other is a simulated image of the universe. Together they suggest the surprisingly similar patterns found in vastly different natural phenomena. DAVID CONSTANTINE

Mark Miller, a doctoral student at Brandeis University, is researching how particular types of neurons in the brain are connected to one another. By staining thin slices of a mouse's brain, he can identify the connections visually. The image above shows three neuron cells on the left (two red and one yellow) and their connections.

An international group of astrophysicists used a computer simulation last year to recreate how the universe grew and evolved. The simulation image above is a snapshot of the present universe that features a large cluster of galaxies (bright yellow) surrounded by thousands of stars, galaxies and dark matter (web).

(Source by Mark Miller, Brandeis University; Virgo Consortium for Cosmological Supercomputer Simulations; www.visualcomplexity.com)

Proteins? Not DNAs

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Marslov, Sergei and Kim Sneppen

Science May 03, 2002

If you took a given number of proteins and distributed interactions among them randomly, you would hardly find any particular protein that would have a lot of interactions. Proteins would all talk randomly with each other in such a network, Maslov says. So, hubs of highly-interacting proteins are not something that you would expect to happen by pure chance.

But the scientists did observe hubs of interacting proteins in the yeast cells. The connections between hub proteins reveal an emergent property that acts beyond the level of the functions of the individual proteins and makes them act together to coordinate their functions. Studying these interactions can help identify these coordinated functions, and may also reveal intrinsic features of the interacting proteins.

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: ?

Network Description
Actors Partition
Actors Position
Statistical Approach

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:

2004. (). . ( )

. 2003. . . ( )

Wasserman, Stanley and Katherine Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.

Knoke, David and James H. Kuklinski. 1982. Network Analysis. Beverly Hills, California: SAGE Publications.

Scott, John. 1991. Social Network Analysis: a handbook. Newbury Park, California: SAGE Publications.

Wellman, Barry and Berkowitz S.D. 1988. Social Structures: A Network Approach. Cambridge: Cambridge University Press.

Degenne, Alain and Michel Forse. 1999. Introducing Social Networks. London: SAGE Publications

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:

Borgatti, Everett and Freeman. 2004. UCINET 6 Users Guide. Harvard, MA: Analytic Technologies.

Burt, Ronald. 1991. STRUCTURE Reference Manual. New York, NY: Center for the Social Sciences Columbia University.

Hanneman, Robart A. 2001. Introduction to Social Network Methods. (included in UCINET 6 package)

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: Internet

http://www.insna.org/

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UCINET
http://www.analytictech.com/

STRUCTURE http://web.yonsei.ac.kr/yoosik/index.htm

PAJEK
http://vlado.fmf.uni-lj.si/pub/networks/pajek/

NETMINER
http://www.cyram.com/

MATLAB, MATHEMATICA

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vs.

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1950 : copper + lead bronze

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- 1

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Usual Suspects:

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vs. :

. . . . . .

- 2004 -

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vs. :

.

-

? -

- 2004 -

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Getting a job: Strength of Weak Ties

Performance: Structural Hole

Diffusion: Cohesion vs. Structural Equivalence

Diffusion: Assortative vs. Dissortative

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Square Matrix

Non-square Matrix

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ABCA001B100C000

rstuA0011B1010C0001

Global Networks:


random sample?Ego-centric Network:

Bi/ Valued NetworkDirected/ Un-directed Network

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Sampling

Representative Sampling: i.i.d. representative of what?

Snowball Sampling: hidden, small population

Respondent Driven Sampling (Heckathorn)

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:

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1100111010110111

X

=

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1100111010110111

1100111010110111

2210322122222232

Network Description - 1

NETWORK DESCRIPTION

Figure: Draw

Basic: Tools>Univariate Stats

Density: Network>Cohesion>Density

Diameter: Network>Cohesion>Distance

Reachability: Network>Cohesion>Reachability

Connectivity: Network>Cohesion>Point Connectivity

Transitivity: Network>Cohesion>Transitivity

Basic: mean ties, s.d. of ties, etc. across actors
Density: (actual # of ties)/ (# of all possible ties)

Diameter: longest geodesic distance in a network

Reachability: 1 if reachable or 0

Connectivity: the number of nodes that would have to be removed in order for one

actor to no longer be able to reach another

Transitivity: if A B and B C, then AC

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: 10 (Knoke)

Network Description - 2

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12345678910101001010102101110111030101111001411001010005111100111160010001010701011000008110110101090100101000101110101000

Figure: Draw

Network Description - 3

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Network Description - 4

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Connectivity

POINT CONNECTIVITY

--------------------------------------------------------------------------------

Input dataset: E:\Program Files\Ucinet 6\DataFiles\KNOKBUR

NOTE: This procedure only operates on the first matrix in a dataset.

1

1 2 3 4 5 6 7 8 9 0

C C E I M W N U W W

- - - - - - - - - -

1 5 5 3 4 5 1 6 4 4 3

2 5 8 3 5 8 1 6 5 3 4

3 3 3 4 4 3 1 4 3 3 3

4 5 5 3 5 5 1 5 4 3 4

5 5 8 3 5 8 1 6 5 3 5

6 1 1 1 1 1 1 2 1 2 1

7 5 6 3 5 6 1 6 4 2 3

8 5 5 3 5 5 1 5 5 4 4

9 3 3 3 3 3 1 3 3 3 3

10 4 5 3 4 5 1 4 4 3 5

Output actor-by-actor point connectivity matrix saved as dataset PointConnectivity

Network Description - 5

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Actors Partition: bottom-up

Clique: Network>Subgroups>CliquesN-clique: Network>Subgroups>N-CliquesK-plexes: Network>Subgroups>K-PlexK-cores: Network>Regions>K-Core

Clique: the maximum number of actors who have all possible ties present among themselves. everybody knows everybody. Maximal complete sub-graph.N-clique: they are connected to every other member of the group at a distance greater than one. Usually, the path distance two is used. This corresponds to being "a friend of a friend." : 2-clique. Maximal sub-graph where largest geodesic is no greater than n. diameter can be larger than n, and thus not so cohesive group.N-clans: first identify n-cliques and exclude those n-cliques that have a diameter larger than nN-clubs: maximal n-diameter graphK-plexes: a node is a member of a clique of size n if it has direct ties to n-k members of that clique. It requires that members of a group have ties to (most) other group members -- ties by way of intermediaries (like the n-clique approach) do not quality a node for membership. K-cores: all of whom are connected to some number (k) of other members of the group. The k-core definition is intuitively appealing for some applications. If an actor has ties to a sufficient number of members of a group, they may feel tied to that group -- even if they don't know many, or even most members.

Actors Partition - 1

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Actors Partition - 2

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Actors Partition: top-down

Components: Network>Regions>ComponentsBlocks: Network>Regions>Bi-ComponentFactions: Network>Subgroups>Factions

Components: sub-graphs that are connected within, but disconnected between sub-graphs.Blocks: if a node were removed, would the structure become divided into un-connected parts? If there are such nodes, they are called "cutpoints." The divisions into which cut-points divide a graph are called blocks (or bi-components). Identify vulnerable parts. Factions: ideally, all sub-groups are cliques and each sub-group is component. factions produce the closest fractions to this ideal sub-groups. You have to specify the number of factions for the estimation.

Actors Partition - 3

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EDUC(3), WRO(6)

4 Factions

Actors Partition - 4

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Actors Position

Degree Centrality: Network>Centrality>DegreeCloseness Centrality: Network>Centrality>ClosenessBetweeness Centrality: Network>Centrality>BetweenessPower: STRUCTUREBonacich Power: Network>Centrality>PowerStructural hole: Network>Ego Networks>Structural HolesStructural Equivalence: : Network>Roles&Positions>StructuralRole Equivalence: STRUCTUREBrokerage: Network>Ego Networks>BrokerageBridgeness: MATLAB PROGRAM

Actors Position - 1

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Three Centralities

Degree: # of ties

Closeness: 1/ (geodesic distance)

Betweeness:

?

1 betweeness: 0

2 betweeness: 11: (1-3), (1-5), , (1-8),

(3-2),(3,4),, (3-8)

Actors Position - 2

10/21= 47.619% (21=7C2)

7/11= 63.636%

3/7= 42.857%

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Burts Power: Prominence - 1

Actors Position - 3

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Burts Power: Prominence - 2

Actors Position - 4

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Burts Power: Prominence - 3

Actors Position - 5

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Bonacichs Power - 1

Rij . power ci .

power . 0 power direct tie .

. (bargaining). , . ( ).

(power index network size normalize ).

power 1 .

Actors Position - 6

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Bonacichs Power - 2

Actors Position - 7

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Bonacichs Power - 3

UCINET .

From Bonacichs Paper

From UCINETs output

MATLAB Bonacich Power .

[B] = Bonacich(data set, 0.3). It will create a vector, B that contains Bonacich index with a correct adjusted .

===========================================

function [B] = Bonacich(p,beta)

le=length(p);

% original index without normalizing factor alpha

ori = inv(eye(le) - beta*p)*p*ones(le,1);

alpha = sqrt (le/ (sum(ori .* ori)));

B = alpha * ori;

====================================================

Actors Position - 8

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Structural Hole - 1

Actors Position - 9

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Structural Hole - 2

Actors Position - 10

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Structural Equivalence

two actors are structurally equivalent to the extent that they have identical relations with every other person , structural equivalent

Actors Position - 11

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Role Equivalence - 1

Actors Position - 12

, , .

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Role Equivalence - 2

Actors Position - 13

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Brokerage - 1

Actors Position - 14

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Brokerage 2: 16

Actors Position - 15

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Brokerage 3

16 :

Actors Position - 16

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(coordiantor)

(representative) (gatekeeper)

(liaison)

(itinerant broker)

Bridgeness 1 (Youm 2007)

1 2 5 4 : (o), trail (o), (o)
1 2 5 6 5 : (o), trail (o), (x)
1 2 1 2 5 : (o), trail (x), (x)

(path): ( ).

Trail: . . .

(walk): , , ( ), / ,

Actors Position - 17

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Bridgeness - 2

,

kf*ij: i k j .

1, i j k 0. 0, k 1:
(1 - kf*ij).

kf*ij (1) i j (2) k .

Actors Position - 18

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Bridgeness - 3

Bridgeness : 1 2 1, 1 2 . : () .

Actors Position - 19

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BetweenessStructural holeBridgeness1010.321130.53010.34010.451530.66102.30.57010.48010.4

Bridgeness 4: hidden bridges

Actors Position - 20

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Sexual Network Approach: two hidden aspects of STD Dynamics

Actors Position - 21

A hypothetical sexual network

A1 A A2 B1 B B2

C

PAGE

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INDIVIDUAL RISK APPROACH

Person A and person B have the same number of partners (two partners). In this sense, person A is as likely to be infected as person B.

NETWORK APPROACH

REVEALED ASPECT 1: Person A is more likely to be infected than person B because person As partners have more sexual partners than person Bs partners. REVEALED ASPECT 2: However, person B is a more efficient (powerful) transmitter than person A because person B is a bridge position between two large sub-populations while person A is inside a clique. Person A is redundant in the transmission path (there is another path from person A1 to person A2 through person C) but without person B being infected, it is not possible for one group transmit infection to the other group so that the whole group to be infected.

Statistical Approach

Log-linear modeling

P* model

Monte-Carlo Method

Actors Position - 22

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Log-linear Modeling

MDS . goodness of fit test odds-ratio built-in

Actors Position - 23

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So what?

We are not what you eat. We are whom we have tie with.

Furthermore, we need global picture to locate our position, which cant be available to our own local eyes.

Social network analysis provides quantitative and mechanism-oriented tools to analyze these ties, and thus ourselves or our world.

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INDIVIDUAL RISK APPROACH

Person A and person B have the same number of partners (two partners). In this sense, person A is as likely to be infected as person B.

NETWORK APPROACH

REVEALED ASPECT 1: Person A is more likely to be infected than person B because person As partners have more sexual partners than person Bs partners. REVEALED ASPECT 2: However, person B is a more efficient (powerful) transmitter than person A because person B is a bridge position between two large sub-populations while person A is inside a clique. Person A is redundant in the transmission path (there is another path from person A1 to person A2 through person C) but without person B being infected, it is not possible for one group transmit infection to the other group so that the whole group to be infected.

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2

1

n

i

i

Cn

=

=

22

11

()(),,

nn

ijiqjqqiqj

qq

dzzzzqij

==

=-+-

36

2

1

()

ijjqiq

q

dtt

=

=-

(coordiantor)(representative) (gatekeeper)

(liaison)

(itinerant broker)

A hypothetical sexual network

A1

A

A2 B1

B

B2

C

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Number of infected people

Figure 4. Sexual distances in 3 dimensional space

Prefix indicates race/etnicity: w for White, b for Black, h for Hispanic

Suffix means activity level: p for Periphery, a for Adjacent, c for core

ba

bc

hc

D

i

m

e

n

s

i

o

n

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1.5

2.0

ha

-1.5

-1.0

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bp

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wc

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Dimension 2

Dimension 1

hp

wa

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wp