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Public defence of my thesis on groups and reputation in social networks (2 september 2013, Louvain-la-Neuve).
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Groups and Reputation in Social Networks
V.A. Traag
Promoteurs:Paul Van Dooren, Yurii Nesterov
Jury:François GlineurVincent BlondelMarco Saerens
Patrick De Leenheer
ICTEAMUniversité Catholique de Louvain
2 September 2013
Soutenance Publique
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
Social networks
I did not analyse these
Keep it simple
Keep it simple
Keep it simple
Keep it simple
Keep it simple
Node or Vertex
Keep it simple
Link or Edge
Keep it simple
Network or Graph
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in community
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in communitymc = 4
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in communitymc = 4
Possible links?
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in communitymc = 4
Possible links?(nc2
)= nc(nc−1)
2 = 4×32 = 6
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in communitymc = 4
Possible links?(nc2
)= nc(nc−1)
2 = 4×32 = 6
4 links in community,2 missing.
What is a community?
0
12
3
4
56
7
8
9
10
11
Community or Cluster
But is it a good community?
Count links in communitymc = 4
Possible links?(nc2
)= nc(nc−1)
2 = 4×32 = 6
4 links in community,2 missing.
Want many links, few missing
What is a community?
0
12
3
4
56
7
8
9
10
11
Bad community
Count links in communitymc = 5
Possible links?(nc2
)= nc(nc−1)
2 = 5×42 = 10
5 links in community,5 missing.
What is a community?
0
12
3
4
56
7
8
9
10
11
Are there better communities?
Make money
0
12
3
4
56
7
8
9
10
11
Get money for communities:
• get 1 − c for every edge in community,
• pay c for missing edge in community.
Make money
0
12
3
4
56
7
8
9
10
11
Get money for communities:
• get 1 − c for every edge in community,
• pay c for missing edge in community.
Suppose c = e0.50
4 edges, 2 missing:4 × 0.5 − 2 × 0.5 = e1.00
Make money
0
12
3
4
56
7
8
9
10
11
Get money for communities:
• get 1 − c for every edge in community,
• pay c for missing edge in community.
Suppose c = e0.50
4 edges, 2 missing:4 × 0.5 − 2 × 0.5 = e1.00
2 edges, 1 missing:2 × 0.5 − 1 × 0.5 = e0.50
Make money
0
12
3
4
56
7
8
9
10
11
Get money for communities:
• get 1 − c for every edge in community,
• pay c for missing edge in community.
Suppose c = e0.50
4 edges, 2 missing:4 × 0.5 − 2 × 0.5 = e1.00
2 edges, 1 missing:2 × 0.5 − 1 × 0.5 = e0.50
5 edges, 5 missing:5 × 0.5 − 5 × 0.5 = e0.00
Make money
0
12
3
4
56
7
8
9
10
11
Get money for communities:
• get 1 − c for every edge in community,
• pay c for missing edge in community.
Suppose c = e0.50
4 edges, 2 missing:4 × 0.5 − 2 × 0.5 = e1.00
2 edges, 1 missing:2 × 0.5 − 1 × 0.5 = e0.50
5 edges, 5 missing:5 × 0.5 − 5 × 0.5 = e0.00
Total: e1.50
Better communities
Initial communities: e1.50
0
12
3
4
56
7
8
9
10
11
Better communities
Initial communities: e1.50
Move 0: get 2 × 0.5 = e1.00 extra
0
12
3
4
56
7
8
9
10
11
Better communities
Initial communities: e1.50
Move 0: get 2 × 0.5 = e1.00 extra
Move 5: get 3 × 0.5 = e1.50 extra
0
12
3
4
56
7
8
9
10
11
Better communities
Initial communities: e1.50
Move 0: get 2 × 0.5 = e1.00 extra
Move 5: get 3 × 0.5 = e1.50 extra
Move 11: get 1 × 0.5 = e0.50 extra
0
12
3
4
56
7
8
9
10
11
Better communities
Initial communities: e1.50
Move 0: get 2 × 0.5 = e1.00 extra
Move 5: get 3 × 0.5 = e1.50 extra
Move 11: get 1 × 0.5 = e0.50 extra
0
12
3
4
56
7
8
9
10
11
Final communities: e4.50
Better communities
Initial communities: e1.50
Move 0: get 2 × 0.5 = e1.00 extra
Move 5: get 3 × 0.5 = e1.50 extra
Move 11: get 1 × 0.5 = e0.50 extra
0
12
3
4
56
7
8
9
10
11
Louvain Algorithm
Real network
My own Facebook
Real network
My own Facebook c = e0.–528 internal links
Real network
My own Facebook c = e0.0002527 internal links
Real network
My own Facebook c = e0.0025526 internal links
Real network
My own Facebook c = e0.01511 internal links
Real network
My own Facebook c = e0.10491 internal links
Real network
My own Facebook c = e0.500 internal links
Resolution limit
Significance
Original partition (14 links)
Significance
Original partition (14 links)
Random graph (5 links)
Significance
Original partition (14 links)
Random graph (5 links) Find partition (11 links)
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
Overview
Social Networks
1 2Community Detection Reputation & Negative Links
Social Balance
+Leonard Sheldon
Social Balance
+
+
Leonard Sheldon
Leslie
Social Balance
+
+ −
Leonard Sheldon
Leslie
Social Balance
+
−−
Leonard Sheldon
Leslie
Social Balance
+
−−
Leonard Sheldon
LeslieThe enemy of my enemy is my friend
Social Balance
+
−−
Leonard Sheldon
LeslieThe friend of my enemy is my enemy
Social Balance
+
−−
Leonard Sheldon
LeslieThe friend of my enemy is my enemy
Socially balanced: +−− = +
Balanced Triads
Balanced Triads
Balanced Triads
Balanced Triads Unbalanced Triads
Balanced Triads
Balanced TriadsTwo Factions
Changing Triads
+
−−
Leonard Sheldon
Leslie
Changing Triads
+
−−+
Leonard Sheldon
Leslie
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
Changing Triads
+
−+
−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
t
Changing Triads
+
−+
−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
t
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
Compare friends with Leslie
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
Compare friends with Leslie
Sheldon likes Leonard +
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
Compare friends with Leslie
Sheldon likes Leonard +
Leslie dislikes Leonard −
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Sheldon likes Leonard +
Leonard likes Leslie +
Effect ++ = +
Compare friends with Leslie
Sheldon likes Leonard +
Leslie dislikes Leonard −Effect +− = −
Changing Triads
+
−−+
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Compare friends with Leslie
Sheldon likes Leonard +
Leslie dislikes Leonard −Effect +− = −
t
Changing Triads
+
−−
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Compare friends with Leslie
Sheldon likes Leonard +
Leslie dislikes Leonard −Effect +− = −
t
Changing Triads
+
−−
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Compare friends with Leslie
Sheldon likes Leonard +
Leslie dislikes Leonard −Effect +− = −
t
Changing Triads
+
−−
Leonard Sheldon
LeslieSheldon’s relationship with Leslie changes
Ask Leonard what to do
Compare friends with Leslie
Does not converge tosocial balance
Does converge tosocial balance
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