This document summarizes research on measuring cross-community influence between online discussion forums. The researchers propose using a membership matrix and centrality matrix to calculate an impact matrix measuring how much communities influence each other. They apply their framework to 10 years of data from Irish discussion boards, identifying the most important and dependent communities over time as well as pairs with high cross-community influence counts. The researchers aim to extend their work with topic analysis and empirically-observed cascades.

1. Digital Enterprise Research Institute www.deri.ie
Cross-Community Influence in
Discussion Fora
Václav Belák, Samantha Lam, Conor Hayes
Stefan.Decker@deri.org
http://www.StefanDecker.org/
© Copyright 2010 Digital Enterprise Research Institute. All rights reserved.

2. Motivation
Digital Enterprise Research Institute www.deri.ie
• Online social communities represent an important cultural and
business asset in context of many services on the Web
• Management and exploitation of these communities has thus become
important and one way to do it is to focus on influential actors
• Social influence has been intensively studied in SNA, but can we extend
the notion of influence to the level of communities?
forum A forum B
5
2
1 4 6
3
7

3. Research Questions
Digital Enterprise Research Institute www.deri.ie
• How can we identify communities persistently affecting other
communities?
• Given a specific community, which communities does it
influence? Which communities are dependent on the activity of
others?
• Over time, how can we identify that a community is being
increasingly influenced or even overtaken by another
community?

4. Methods: Definition of Impact
Digital Enterprise Research Institute www.deri.ie
• We propose to take two factors into account:
1. degree of community membership of the users
2. centrality of the users within each community
• we used in-degree (# replies of a user)
• For general case of n users and k communities define:
• n × k membership matrix M
• n × k centrality matrix C
• Cross-community k × k impact matrix J can then be obtained as a product
of the two matrices: ! 1
#
0 $
&
! 2
#
0 $
&
M = # 0.2 0.8 &, C = # 10 10 &
# 0 1 & # 0 5 &
" % " %
! 4 2 $
J = M TC = # &
" 8 13 %
• Communities have usually different sizes, we therefore work with
normalised impact matrix: J
ˆ
Ji, j = n i, j
! Ml,i l=1

5. Methods: Impact-based Measures
Digital Enterprise Research Institute www.deri.ie
• Diagonal elements of J contain independence
values (self-impact)
! 4 2 $
J =# &
• Total impact a community has on others
is its importance
" 8 13 %
• Total impact other communities have on a community
is the community’s dependence
• Level of dispersion (heterogeneity) of importance/dependence of
community i can be measured as an entropy of a an i-th row/column of the
impact matrix
• Is a community broadly influential or does it influence only few other
communities?

6. Evaluation Data-Set
Digital Enterprise Research Institute www.deri.ie
• 10 years of data of the largest Irish discussion board system
• Segmented using 1 week sliding window
• 1 week window represents approx. 84% of cross-fora posting
activity
• 448 snapshots in total
• 636 communities, 73k users, 8M posts

7. Clustering Fora By I. and D.
Digital Enterprise Research Institute www.deri.ie
Aggregate impact matrices from the individual snapshots
and cluster the communities (by k-means) embedded in
the row and column spaces of the aggregate matrix.
● ●
7
●
4
2.5
●
! 1 2 $ 2 ! 133
5 2 $
●
●
●
●
ˆ
J1 = # ˆ82 ●
&, J = #
●
&
●
●
●
●
2.0
● ●
● ●
● ● ●
3
2 4 6 8 10
" 3 3 % " 3 5 %3 5 7 9
log(dependence)
log(importance)
●
1.5
●
●
ˆ ˆ
J1 + J 2 ! 3 2 $
2
ˆ
J agg = =#
1.0
&
2 " 3 4 %
1
0.5
0.0
0
0.3 0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7 0.8
row entropy column entropy

8. Overall I/D over Time
Digital Enterprise Research Institute www.deri.ie
Take the communities with the highest importance and
dependence at each week and plot them over time.
Role Playing After Hours
Films
Games
Computers & Tech. Quake
Sports
After Hours
Literature
Half−Life
Work & Jobs
Webgames
Humanities
Recycle Bin Computers & Tech.
Humour
Television
Reaver Humanities
Help Desk
Science
Feedback
Newbies & FAQ Humour
Freemasons
Moderators
Comeonbanus Counter−Strike
Lord of the Rings
PearTree House
History & Heritage
Digital Art & Design Help Desk
The Illuminati
FNWAI
Tipp Inst IrelandOffline
The Thunderdome
HoLL
Ask Doctor Demento
Lubnip
Politics
The Cuckoo's Nest
Events
Spell Czechs Soccer
Knights of the R.T.
PBAN
Week 1
Week 25
Week 50
Week 75
Week 100
Week 125
Week 150
Week 175
Week 200
Week 225
Week 250
Week 275
Week 300
Week 325
Week 350
Week 375
Week 400
Week 425
Week 1
Week 25
Week 50
Week 75
Week 100
Week 125
Week 150
Week 175
Week 200
Week 225
Week 250
Week 275
Week 300
Week 325
Week 350
Week 375
Week 400
Week 425
Color Key
Color Key
0 0.2 0.4 0.6 0.8
0 0.05 0.1 0.15 0.2 0.25 0.3
Value Value

9. Cross-Community Infl. over Time
Digital Enterprise Research Institute www.deri.ie
Count cases when community i’s impact on j was higher
than j’s independence and plot the pairs with the highest
counts.
Count From (i) To (j)
29 Moderators Reported Posts
22 FNWAI Poker
17 The Thunderdome After Hours
14 PI Mods Personal Issues

10. Moderation of Pers. Issues
Digital Enterprise Research Institute www.deri.ie
7
PI Mods ●
Moderators
independence
6
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5
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4
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impact
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3
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2
●
1
0
150 200 250 300 350 400 450
week

11. Conclusion
Digital Enterprise Research Institute www.deri.ie
• The evaluation demonstrated that the framework
• is able to identify highly influential and dependent communities
• can be used for efficient monitoring of the cross-community
activity, perhaps even for early alerts
• can identify which communities to stimulate (e.g. by posting a
message) s.t. the stimulus spreads efficiently
• We aim to extend it with content analysis
• E.g. What are the most influential communities with respect to a
particular topic?
• We will also investigate empirically-observed topic cascades and modify
our models accordingly if needed
• Finally, our goal is to propose a method for measuring significance of
cross-community impact
• Belák V., Lam S., Hayes C. Cross-Community Influence in Discussion
Fora. ICWSM 2012.
• Belák V., Lam S., Hayes C. Targeting Communities to Maximise
Information Diffusion. MSND/WWW 2012.

12. Fold, No, Wait, All In!
Digital Enterprise Research Institute www.deri.ie
● FNWAI to Poker
Poker to FNWAI
Poker's indep.
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10
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impact
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5
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0
240 260 280 300 320 340
week