# Random walk-based ranking in signed social networks: model and algorithms

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## Abstract

How can we rank nodes in signed social networks? Relationships between nodes in a signed network are represented as positive (trust) or negative (distrust) edges. Many social networks have adopted signed networks to express trust between users. Consequently, ranking friends or enemies in signed networks has received much attention from the data mining community. The ranking problem, however, is challenging because it is difficult to interpret negative edges. Traditional random walk-based methods such as PageRank and random walk with restart cannot provide effective rankings in signed networks since they assume only positive edges. Although several methods have been proposed by modifying traditional ranking models, they also fail to account for proper rankings due to the lack of ability to consider complex edge relations. In this paper, we propose Signed Random Walk with Restart (SRWR), a novel model for personalized ranking in signed networks. We introduce a signed random surfer so that she considers negative edges by changing her sign for walking. Our model provides proper rankings considering signed edges based on the signed random walk. We develop two methods for computing SRWR scores: SRWR-Iter and SRWR-Pre which are iterative and preprocessing methods, respectively. SRWR-Iter naturally follows the definition of SRWR, and iteratively updates SRWR scores until convergence. SRWR-Pre enables fast ranking computation which is important for the performance of applications of SRWR. Through extensive experiments, we demonstrate that SRWR achieves the best accuracy for link prediction, predicts trolls \(4\times \) more accurately, and shows a satisfactory performance for inferring missing signs of edges compared to other competitors. In terms of efficiency, SRWR-Pre preprocesses a signed network \(4.5 \times \) faster and requires \(11 \times \) less memory space than other preprocessing methods; furthermore, SRWR-Pre computes SRWR scores up to \(14 \times \) faster than other methods in the query phase.

## Keywords

Signed networks Signed random walk with restart Personalized node ranking Trustworthiness measure## Notes

### Acknowledgements

This work was supported by Institute of Information & Communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) [2013-0-00179, Development of Core Technology for Context-aware Deep-Symbolic Hybrid Learning and Construction of Language Resources]. The Institute of Engineering Research at Seoul National University provided research facilities for this work. The ICT at Seoul National University provides research facilities for this study.

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