1. Malik Magdon-Ismail, Konstantin Mertsalov, Mark Goldberg
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 Construct sequence of comment graphs (every week)
Alice’s Blog
Bill’s Blog
Alice Posted
Bill Posted A
Bill commented
Alice commented
Cory
commented
Edges:
(A,B); (C,B)
(D,B)
Edges:
(B,A); (C,A)
Alice commented
Cory commented
Dave commented D B C
Construct sequence of comment graphs (every week) 3

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 4

5. Diffusion in Dynamic Networks
Time: T
Time: T+1
Time: T+2 A B F E H C D G J A B F E H C D G J A B F E H C D G J
Static C A B F E H C D G J A B F E H C D G J 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. Network at iteration t+1
Modeling Dynamics
Input
Network at iteration t
Output
Network at iteration t+1 C C A A B D B D E J E J F F H H G G

9. Step 2: Local Attachment
A General Model
Input: Gt
Step 1: Find Locality C A C B A D B D F E J F E J H G H G
Step 2: Local Attachment
Output: Gt+1 C A B C D A B D F E J F E J H G H G

10. 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
Uniform
Preferential Attachment
Random walk D
Gt+1 F E J H G
* Community = union of overlapping clusters [Baumes, Goldberg, Magdon-Ismail 2005]

11. Diffusion Models Linear Threshold:C C
Linear Threshold:
Node i has a susceptibility fraction T(i).
Node i infected if at least T(i) neighbors are infected. A A B B D D F F E J E 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 J E J
0.4 H H G G

12. Diffusion in Dynamic Network
Diffusion Model
Network Dynamics
Cascade
Real LiveJournal
Diffusion
Progression
Locality and
Attachment
Threshold
Model

13. Static Aggregated Network
Results
Dynamic Network
Static Aggregated Network
Cascade
Threshold

14. Conclusions
Dynamics of the network strongly affects it’s diffusion properties
Global random link dynamics does not model dynamics correctly
Social network links evolve through locality (social groups), eg. cluster-based communities+PA produces diffusion faithful network dynamics.

15. Thank you !