We investigate the "negative link" feature of social networks that allows users to tag other users as foes or as distrusted in addition to the usual friend and trusted links. To answer the question whether negative links have an added value for an online social network, we investigate the machine learning problem of predicting the negative links of such a network using only the positive links as a basis, with the idea that if this problem can be solved with high accuracy, then the "negative link" feature is redundant. In doing so, we also present a general methodology for assessing the added value of any new link type in online social networks. Our evaluation is performed on two social networks that allow negative links: The technology news website Slashdot and the product review site Epinions. In experiments with these two datasets, we come to the conclusion that a combination of centrality-based and proximity-based link prediction functions can be used to predict the negative edges in the networks we analyse. We explain this result by an application of the models of preferential attachment and balance theory to our learning problem, and show that the "negative link" feature has a small but measurable added value for these social networks.

1. What Is the Added Value of Negative
Links in Online Social Networks?
Jérôme Kunegis, Julia Preusse, Felix Schwagereit
Institute for Web Science and Technologies (WeST), University of Koblenz–Landau
We thank Paolo Massa for providing the Epinions dataset. The research leading to these results has received funding from the
European Community's Seventh Framework Programme under grant agreement n° 257859, ROBUST.

2. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 2
Social Networks: Ties between People

3. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 3
Some People Don't Like Each Other

4. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 4
Real Social Networks Contain Negative Ties

5. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 5
Online Social Networks Have Many Forms of Positive Links

6. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 6
Where Are the Negative Ties?

7. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 7
They Are on Slashdot.org
79,120 users; 392,326 positive ties; 123,255 negative ties
http://konect.uni-koblenz.de/test/networks/slashdot-zoo
[1] J. Kunegis, A. Lommatzsch, C. Bauckhage. The Slashdot Zoo: Mining a Social
Network with Negative Edges. In Proc. WWW, pages 741– 750, 2009.

8. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 8
And Epinions.com
131,828 users; 717,667 positive ties; 123,705 negative ties
http://konect.uni-koblenz.de/networks/epinions
[2] P. Massa, P. Avesani. Controversial users demand local trust metrics: an
experimental study on epinions.com community. In Proc. AAAI, pages 121– 126, 2005.

9. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 9
What Is the Added Value of Negative Links?
Pro: More information about the community
Con: More negativity in the community

10. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 10
Pro: More information about the community
Really?
What Is the Added Value of Negative Links?

11. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 11
Our Idea
If negative links can be predicted from positive ones, then
negative links do not
bring any added
value to the network

12. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 12
Machine Learning Task
Prediction

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Related Problem: Prediction of Future Ties (Link Prediction)
Prediction

14. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 14
Indicators for Link Prediction
?
Neighborhood-basedCentrality-based
➔Common neighbors
➔Cosine similarity
➔Jaccard coefficient
➔Adamic–Adar
➔Exponential/Neuman graph kernel
➔Paths of length 3
➔Degree
➔PageRank

15. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 15
Centrality-based Indicators
Degree
PageRank
u v
f(u, v) = d(u) d(v)
f(u, v) = PR(u) PR(v)

16. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 16
Neighborhood-based Indicators
Common neighbors
Jaccard index
Cosine similarity
A
B
u v
f(u, v) = |A Ո B|
f(u, v) = |A Ո B| / |A U B|
f(u, v) = |A Ո B| / sqrt(|A| |B|)

17. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 17
Link Prediction: Edge vs No Edge
?
tie
no tie

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Our Task: Positive Edge vs Negative Edge vs No Edge
?
pos. tie
neg. tie
no tie

19. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 19
A Good and Simple Idea Which Does Not Work
?

20. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 20
Learning Feature Weights by Regression
Dataset Degree PageRank Common
neighbors
Paths of
length 3
Cosine
similarity
Slashdot 0.2502 0.2321 −0.5411 −0.4866 −3.9434
Epinions −0.0105 0.8498 −0.8587 −0.3827 −5.0360
Centrality-based Neighborhood-based
Preferential
attachment
holds for
negative edges
Conflict
is avoided

21. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 21
Measuring Prediction Accuracy
(1) Neg-tie vs Pos-tie + No-tie
(2) Neg-tie vs No-tie
(3) Neg-tie vs Pos-tie

22. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 22
Prediction Accuracy

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Let's Look at the Data
Slashdot Epinions

24. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 24
Combine PageRank and Cosine Similarity
f = ® ({ ) − ¯ log(cos)
log(PR) if cos = 0
min(log(PR)) otherwise
Slashdot Epinions

25. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 25
Evaluation
All >0.5

26. Jérôme Kunegis et al. What Is the Added Value of Negative Links in Online Social Networks? 26
How Much Better Does It Get If We Have Negative Links?
The “enemy” function
adds 0.05 points
of AUC to knowing
negative ties

27. http://konect.uni-koblenz.de/
Add a (positive?) link to me on Twitter!
@kunegis
Thank You!