Models of Communication Dynamics for Simulation of Information Diffusion

1
Models of Communication Dynamics for Simulation
of Information Diffusion

• Malik Magdon-Ismail, Konstantin Mertsalov, Mark
  Goldberg

2
Motivation

• Important to understand information diffusion in
  social networks
• Viral marketing, gossip, rumors, etc.
• Social Networks are dynamic
• Edges and nodes change with time.
• Cannot repeat historical dynamics, so need to
  simulate dynamics for research.

3
LiveJournal Data
Alices Blog
Bills Blog
Alice Posted
Bill Posted
A

• Bill commented
• Alice commented
• Cory
• commented

Edges (A,B) (C,B) (D,B)

• Alice commented
• Cory commented
• Dave commented

Edges (B,A) (C,A)
B
D
C
Construct sequence of comment graphs (every week)
4
Dynamics of LiveJournal Network

• 60 weeks
• Per week
• 153,028 nodes
• 510,317 edges
• Very dynamic
• 70 of edges change from week to week

5
Diffusion in Dynamic Networks
Time T
Time T1
Time T2
Static
C
A
B
D
Dynamic
F
E
J
H
G
6
Diffusion in LiveJournal Blogs
Linear Threshold
Independent Cascade
Diffusion model and network dynamics have a big
impact on infection.
7
Goal

• Can we model the network dynamics so that
  diffusion in the model mimics diffusion in the
  real network?

8
Modeling Dynamics
Output Network at iteration t1
Input Network at iteration t
C
C
A
A
B
D
B
D
E
J
F
E
J
F
H
H
G
G
9
A General Model
Input Gt
Step 1 Find Locality
C
C
A
A
B
D
B
D
F
E
J
F
E
J
H
H
G
G
Step 2 Local Attachment
Output Gt1
C
A
B
C
D
A
B
D
F
E
J
F
E
J
H
G
H
G
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Ingredients to General Model
1. What is the locality of the node ?
C
A

• Global all nodes
• k-Neighborhood
• Community

B
D
Gt
F
E
J
H
G
2. How to attach within locality ?
C
A
B
D

• Uniform
• Preferential Attachment
• Random walk

Gt1
F
E
J
H
G
Community union of overlapping clusters
Baumes, Goldberg, Magdon-Ismail 2005
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Diffusion Models
C
C
A
A

• Linear Threshold
• Node i has a susceptibility fraction T(i).
• Node i infected if at least T(i) neighbors are
  infected.

B
B
D
D
F
F
E
E
J
J
H
H
G
G
C
C
A
A

• Independent Cascade
• Every edge (i,j) has transmission prob. P(i,j).
• Nodes have one chance to infect neighbors.

B
B
D
D
0.3
0.2
F
F
E
E
J
J
0.4
H
H
G
G
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Diffusion in Dynamic Network
Diffusion Model
Network Dynamics
Real LiveJournal
Cascade
Diffusion Progression
Locality and Attachment
Threshold
Model
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Results
Dynamic Network
Static Aggregated Network
Cascade
Threshold
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Conclusions

• Dynamics of the network strongly affects its
  diffusion properties
• Global random link dynamics does not model
  dynamics correctly
• Social network links evolve through locality
  (social groups), eg. cluster-based communitiesPA
  produces diffusion faithful network dynamics.

15
Thank you !