1. Joint Community and Structural Hole Spanner Detection via Harmonic Modularity
Lifang He
College of Computer Science and Software Engineering
Shenzhen University, China
Hello everyone, this is Lifang He, now I will introduce our KDD paper for you.

2. Core Research in Social Network[1]
The topic is about social network. Please look at the picture, this is a top level view of core research in social network. Community and structural hole spanner are two important notions in social network, and naturally tangled with each other. However, these two notions are often studied independently.
[1] T. Lou and J. Tang. Mining Structural Hole Spanners Through Information Diffusion in Social Networks. In WWW'13 Slide.

3. Intuitions Community & Structural hole spanner.
“Holes” exists between communities that are otherwise disconnected[2].
Structural hole spanners control information diffusion between communities.
Community 1
Community 2
Community 3
Information
diffusion
Structural Hole Spanner
To summarize the observation, we have 3 intuitions,
1) …
2) …
Based on these three intuitions, we design HAM and SHII.
What are relationships between “community” & “structural hole spanner”?
They are naturally tangled with each other
Well, community & structural hole spanner are naturally tangled with each other…
[2] R. S. Burt. Structural Holes: The Social Structure of Competition. Harvard University Press, 1992.

4. Today, let us start with the joint study of “community” &“structural hole spanner”…
Three parts
we want to connect these two notions together

5. Overview

6. Overview
Study an interesting problem : joint community & structural hole spanner detection.
Propose a harmonic modularity model (HAM) to simultaneously detect community and structural hole spanner in social networks, and provide a metric (SHII) to evaluate the quality of discovered structural hole spanners.
Results
HAM performs well on both community detection and structural hole spanner detection.
SHII is an effective measure for evaluating the structural hole spanners.
We provide a unique insight into the joint notions of community and structural hole spanner.
In the work, we study an interesting problem: joint community & structural hole spanner detection
We propose a harmonic modularity model (HAM) to deal with this problem and discover an interesting metric to evaluate the quality of discovered structural hole spanners. This provides a unique insight into the joint notions of community and structural hole spanner.

7. Key Innovations
I would like to clarify our main contributions, since this has been stated separately in the paper.

8. Algorithm – Harmonic Modularity
INPUT :
-- A social network, G = (V, E)
Identifying m communities C = (C1, C2, …, Cm) and top-k structural hole spanners
Which node is the best structural hole spanner?
F : community & Top-k structural holes spanners indicator
Objective function: measure the harmonic level between the node and its neighbors.
L21-norm: enforce row-wise sparsity of F to discriminate relevant top-k structural hole spanners.

9. Algorithm – Harmonic Modularity
NOTE: How to get m communities and top-k structural hole spanners from F.

10. Metric – Structural Hole Influence Index
Numerator:
measure the number of influenced outsiders.
measure a metric based on the flow of information through the mined spanner candidates for some commonly studied information diffusion models
Denominator:
measure the number of influenced nodes
(insiders & outsiders).
NOTE: It is important to consider both numerator & denominator in the SHII.
SHII depends heavily on the applied information diffusion model.

11. Results

12. Experiment
# Node
# Edge
## SH spanner
# Community
Karate Club 34 78 13 2
DBLP
1557.6±362.19
4915.6±451.95
189±49.44
15±4.24
YouTube
1310±133.67
2853.5±289.69
91.3±13.57
15.25±2.06
GOAL: Community detection & Structural hole spanner detection

13. Structural Hole Spanner Detection
The results indicate our proposed method can guarantee to find more positive SH spanners connecting to different communities.
Information diffusion model
times better

14. Case study on the karate club network
Visualization: Nodes with mark O
represent structural hole spanners
An example: finding top 3 structural holes
HAM captures the most intermediate nodes between communities.
Other methods tend to take the highest degree nodes as structural hole spanners.

15. Community Detection Clear Improvement Better
Now, I turn to discuss how structural hole spanners can help community detection.
Specifically, we consider community detection, before and after removing the top-k SH spanners discovered by our method
These results provide a strong evidence for the effectiveness of our proposed method for community detection.

16. Efficiency
Converge around only 20 iterations.
Efficient!!

17. Future works Learning from overlapping social networks.
Learning from heterogeneous social networks.
Learning from dynamic social networks.
For future works, first, we want to use the resulting algorithm as a reference localization for more complex social network analysis, such as overlapping social network, heterogeneous social network and dynamic social network.
Second, as the proposed evaluation metric - Structural Hole Influence Index depends heavily on the applied information diffusion model, we will elaborate on a cross evaluation metric for structural hole spanner detection.

18. Thanks you！ Collaborators: Chun-Ta Lu (UIC)
Jiaqi Ma (THU), Jianping Cao (NUDT),
Linlin Shen (SZU), Philip S. Yu (UIC & THU)
Download Paper & Slide:
Finally, I want to thank you my collaborators.
Here we provide a direct link to download the paper and slide. Thank you!