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?

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Community or Cluster

What is a community?

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56

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Community or Cluster

But is it a good community?

What is a community?

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12

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56

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Community or Cluster

But is it a good community?

Count links in community

What is a community?

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12

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56

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Community or Cluster

But is it a good community?

Count links in communitymc = 4

What is a community?

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56

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Community or Cluster

But is it a good community?

Count links in communitymc = 4

Possible links?

What is a community?

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56

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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

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56

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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

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9

10

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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

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56

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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?

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12

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56

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Are there better communities?

Make money

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Get money for communities:

• get 1 − c for every edge in community,

• pay c for missing edge in community.

Make money

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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

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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

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56

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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

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56

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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

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Better communities

Initial communities: e1.50

Move 0: get 2 × 0.5 = e1.00 extra

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56

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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

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56

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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

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56

7

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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

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56

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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

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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