Download Gilad Ravid: Scale Free and Small Worlds Networks: Studying A

Scale Free and Small
Worlds Networks: Studying
A-Synchronous Discussion
Groups
Gilad Ravid
Open University of Israel &
Haifa University
[email protected]
Asynchronous discussion groups
as Small World and Scale Free
Networks by Gilad Ravid and
Sheizaf Rafaeli
September Issue first
pick
http://www.firstmonday.org/issues/issue
9_9/ravid/index.html
Social Network Analysis
SNA
Network analysis is the study of social relations among a
set of actors. It is a field of study -- a set of phenomena
or data which we seek to understand
326
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129 119
150
66 73 55
100
29 31 20
10
3
7
1
1
0
1
50
0
1970
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2002
0
2004

Small World Networks
 Two

characteristics
A small average path length
• Mean shortest node-to-node path

A large clustering coefficient
• How many of a node’s neighbors are connected to
each other
Scale Free Networks
networks are characterized by
a power-law distribution of a node’s
degree.
Number of nodes with k links
 Scale-free
Very many
nodes with few
links
Few nodes with
large # of links
k
Some Published Networks (adapted from
Newman 2003)
social
n
m
Z
l
α
C
film actors
U
449,913 25,516,48
2
113.43
3.48
2.3
0.78
company
directors
U
7,673
14.44
4.6
-
0.34
math
coauthorship
U
253,339 496,489
3.92
7.57
-
0.56
Email
messages
D
59,912
1.44
4.95
1.5/2 0.16
.0
55,392
86,300
sexual contacts U
2,810
Discussion
Groups
D
8,830
info
Word cooccurrence
U
460,902 17,000,00
0
70.13
tech
Internet
U
10,697
31,992
5.98
power grid
U
4,941
6,594
Neural
D
307
2,359
bio
3.2
30,635
4.6
1.3/1 0.08
.4
2.7
0.44
3.31
2.5
0.39
2.67
18.99
-
0.08
7.68
3.97
-
0.28
Small World Networks Affects

CPL -> Information percolation / Speed of
Diffusion

Cliquishness
Personal problems



Find jobs
Find information / answers

Group problems

Disasters recovery
 Inventions

Group decision making

Hard to forecast network dynamics
Scale-Free Networks
 ….
are common
 … important category in networks study
 Have very connected members (Hubs)
 Hubs have a key role
 ….results of self organized network
 … growth with preferential attachment
mechanism
Scale Free Networks Affects
 Continuous
hierarchy of members
 No characterized member
 Resistance to failure
 Sensitivity to attacks
 We know how they form
 Information diffusion
 Rich get richer
Research Sample
 Discussion
groups of more than 400
courses
 Courses taught 1999-2002
 158,276 messages
Why discussion groups?

The main carriage for cooperative learning
and working
 Knowledge management





Sage on the Stage to Guide on the Side
Shared memory (space)
Equal opportunity to read and write messages
Message are the links between participants and
knowledge
One can read (lurk) other discussions
Research populations
The Population
Number
Percentage
of
A All Registered Participants
75,409
100%
A
B Participants who sent at least 1
message
12,506
16.5%
A
C Non active Participants
3,609
(received no answers and did
not answer others)
28.8%
B
D Participants who only answered
themselves
67
0.5%
B
E Regular Participants
8,830
70.6%
B
Frequency  b0  Degree
 b1
Model
b0
b1
R2
Sig. R
Output
Degree
647.469
-1.3125
0.812
0.000
Input Degree 5389.80
-1.9372
0.929
0.000
1915.51
-1.4773
0.826
0.000
All Degree
Out Degree
10000
-1.3125
Frequency (Log)
y = 647.47x
R2 = 0.812
1000
100
10
1
1
10
100
Out Degree (Log)
1000
10000
All Degree
10000
y = 1915.5x-1.4773
2
R = 0.8263
Frequency (Log)
1000
100
10
1
1
10
100
All Degree (Log)
1000
10000
CPL
CC
Discussion Groups Network
4.66618
0.085
Random Network (Average encompassing
three networks)
7.3625
0.000
Theoretical Random Network
7.3045
0.0003928
Ratio between random network and
discussion groups
0.63
216
Creation of a scale-free net
 Growth
and preferential attachment
Scale-Free Networks: Mechanisms
1. Growth
2. Preferential Attachment
Gilad Ravid
[email protected]
http://www.ravid.org/gilad
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