1. A Locality Model of the Evolution of Blog Networks

2. Blog Networks Increasingly important communication forum
Size
Ease of communication
Global
Can represent as a graph
LiveJournal Blog network
15+ million worldwide users
500,000 Russian users
Very dynamic
11/24/2018
IEEE ISI 2008, Taipei

3. Goal Social Network: directed graph
Evolution: sequence of directed graphs
We wish to model evolution
11/24/2018
IEEE ISI 2008, Taipei

4. Why Model Evolution
Contagion processes are different on static vs. dynamic networks.
Information flow on the blogs
Rumors
Advertising and viral marketing
High value nodes in contagion processes
Dynamic
Static A C B A C B A C B A C B A C B A C B
11/24/2018
IEEE ISI 2008, Taipei

5. Growth vs. Evolution Growth Evolution Add new nodes Links static
Given node out degrees
Model specifies where to attach upon node arrival
eg. growth of internet
Preferential attachment
Power-law degree distributions
Evolution
Node set static
Links change
Given node out degrees
Model specifies where to re-attach at each time step
eg. evolution of blog-network communications
Preferential attachment?
Power-law degree distributions?
11/24/2018
IEEE ISI 2008, Taipei

6. Blog-Networks are very Dynamic
150,000 users each week
500,000 communications each week
350,000 are new
70% edges are new each week
11/24/2018
IEEE ISI 2008, Taipei

7. Stability: the in-degree distribution
Other stable statistics: power-law exponent; clustering coef; av. path length; largest component; community structure;…
Stability despite extreme communication dynamics
11/24/2018
IEEE ISI 2008, Taipei

8. Modeling Evolution of BlogsC C A A B B J J D D E E F F H H G G
BlogNetwork(t)
BlogNetwork(t+1)
MODEL
11/24/2018
IEEE ISI 2008, Taipei

9. Testing Models Iterate model to stability
Observed stable statistics should be stable in the model
In-degree distribution
Values of stable statistics should match observed values
Stable power-law in-degree distribution resulting from evolution
11/24/2018
IEEE ISI 2008, Taipei

10. Global Preferential Re-AttachmentJ D
Power Houses Appear E F H G
BlogNetwork(t)
BlogNetwork(t+1)
GPRA
11/24/2018
IEEE ISI 2008, Taipei

11. General Locality Based Model
1. Given:
BlogNetwork at previous time step
Node-Outdegrees A B F E H C D G J
11/24/2018
IEEE ISI 2008, Taipei

12. General Locality Based Model
2. Every node determines its “social” locality A B F E H C D G J
LOCALITY
11/24/2018
IEEE ISI 2008, Taipei

13. General Locality Based Model
3. Every node re-attaches its edges inside its “social” locality. C A B J D E F
ATTACHMENT H G
11/24/2018
IEEE ISI 2008, Taipei

14. Locality and Attachment
Attachment Mechanism
Uniformly random
Preferential Attachment
Erdos-Reyni
random graph
GPRA
Global
Locally random
neighborhoods
Locality
Local-PRA
2-Neighborhood
Community
(Union of Social Groups*)
Locally random
communities
Community-PRA
*Social group = cluster [Baumes, Goldberg, Magdon-Ismail 2005]
11/24/2018
IEEE ISI 2008, Taipei

15. Preferential attachment
Results
Model Errors
Random
Preferential attachment
2-neighborhood
0.503
0.814
Community
0.759
0.154
Global
1.148
0.822
Significance: 0.038
11/24/2018
IEEE ISI 2008, Taipei

16. Summing Up
Modeling blog dynamics is important for information and contagion diffusion.
Simple GPRA does not reproduce stable power-law distributions
Community-PRA gives best model
Other stable statistics for improving models:
Cluster coefficient
Community structure
Fat tail
Path lengths
11/24/2018
IEEE ISI 2008, Taipei

17. Thank You! http://www.cs.rpi.edu/~magdon
SHAMELESS ADVERTISEMENT
ADN 2008: International Workshop on Analysis of Dynamic Networks
(in conjunction with IEEE ICDM 2008)
11/24/2018
IEEE ISI 2008, Taipei