1. A Viewpoint-based Approach for Interaction Graph Analysis
Sitaram Asur and Srinivasan Parthasarathy
Department of Computer Science and Engineering
Ohio State University,
Columbus, Ohio

2. Motivation
Massive social network datasets give you both more and less [Kleinberg, 2007]:
More: can observe global phenomena that are genuine, but literally invisible at smaller scales.
Less: Don’t really know what any one node or link means. Easy to measure things; hard to pose nuanced questions
Community-based analysis useful but limited
All nodes in clusters generally treated the same
Problem : To extract the local neighborhood of interest for a node
To use structure and topology to quantify local relationships
To observe effect of changes in the graph from the viewpoint of given node or set of nodes
Potentially useful in search, recommendation and advertising

3. Viewpoint Neighborhood (VPN)
VPN(S) : the graph rooted at source node S containing only nodes with some degree of importance to S and their interconnections.
But how to measure importance ?
Initial Solution : Use distance from source
Depth-limited VPN for a node
Subgraph representing the set of nodes reachable at a distance <=k from the node and the interactions among them
Can be constructed using Depth-limited search (DLS) from the source node
But is this enough?

4. Viewpoint Neighborhoods
Problems with Depth-limited VPN
All nodes the same distance away are treated the same
Hub nodes need to be differentiated
Criteria for constructing a VPN
Inverse Distance Weighting:
Involvement of a node to a VPN inversely proportional to its distance from the source node
Intuition : Node is more affected by closer events
Link Structure:
Local topological information is important
Well-connected nodes in the VPN are more important to source node
Hub Nodes:
Hub nodes can bloat neighborhoods by bringing in many unimportant nodes
Need to expand hub nodes with low probability

5. Activation Spread Model
Source node begins activation with a budget M
It distributes M among its immediate neighbors activating them
Each node retains some amount, activates its neighbors and continues the distribution
Distribution handled by Activation Function
Each node is activated at most once
If a node is touched more than once, it retains the amount it receives
Threshold used to hasten convergence
Activated nodes form the VPN of source node
Value present with each node represents its commitment value for VPN
Related to the heat diffusion model for graphs

6. Betweenness-based Activation
Activation Functions
Inverse-degree Activation
Down-weights nodes with high degrees
Each node x retains 1/degree(x) of the amount received
Rest distributed equally among its descendants
Strong emphasis on hubs
Weaker emphasis on link structure
Betweenness-based Activation
Compute local betweenness values for nodes within VPN
Consider shortest paths between source node and members of the VPN
Ratio of betweenness values used to distribute
Strong emphasis on link structure
Can be made to handle hubs by using inverse-degree to construct basic VPN first
M/2
M/2
M/6
5M/6
M/6
M/6
M/6
M/2
Inverse Degree Activation
Betweenness-based Activation

7. Activation Functions Semantic Activation
Use semantic features from content to extract neighborhoods
Semantic similarity w.r.t source used to decide distribution ratios
Eliminates noise and irrelevant nodes
Useful in personalized and keyword search applications
In practice, combination of different activation functions can be employed
Domain-specific features can be included

8. Neighborhood Sizes - Wikipedia
Time
Number of Nodes 1
6133 2
24160 3
56468 4
105829 5
147079
Global increase (23x) in number of nodes does not affect size of local neighborhoods too much!

9. Temporal Analysis for VPNsD C B A S
Characterize evolution of Viewpoint neighborhoods over time
Critical Events
Grow
Shrink
Continue
Mutate
Attraction
Repulsion E C H G A B S G H E F C S D C A B S
DBLP : grow/shrink ratio ~1, low continue, high mutate, attract/repel ratio ~ 1
Wikipedia : grow/shrink ratio >>1, high continue events, attract >> repel

10. Behavioral Measures
Incremental behavioral measures composed from events
Stability, Sociability, Impact, Popularity

11. Conclusions Viewpoint Neighborhoods
To identify a neighborhood of interest for a node and quantify local relationships within
General activation spread model with different activation functions capturing topological, semantic and domain-specific attributes
Extension to find the joint VPN of a group of nodes
Evolutionary analysis to identify changes to VPNs over time
Critical events to define behavior of neighborhoods
Behavioral measures for sociability, stability, impact and popularity
Pattern mining over VPNs
Core Subgraphs to identify core influential structures w.r.t certain nodes
Transformation Subgraphs to measure the effect of changes on the graph on specific viewpoint neighborhoods

12. Acknowledgements Grants: NSF: CAREER-IIS-0347662
NSF SGER Grant IIS
DOE: DE-FG02-04ER2561