Ranking In Signed Networks
The well-known Page Rank algorithm is a commonly used tool to rank webpages. On a high level, it determines a new rank for a page based on the current ranks of all of the pages that point to it. You then iteratively compute new ranks based on old ranks until the algorithm terminates. This computes a good measure of how valuable other pages think that a page is, with links from more valuable nodes being weighted more heavily. However, this algorithm does not allow for nodes to explicitly distrust other nodes. Modeling distrust in a network is useful. For instance, you may have a social networks with both positive and negative votes, and you may want to compute popularity in this network.
A naive extension of page rank to deal with this is to separate the graph into positive and negative subgraphs. Given these subgraphs, you run Page Rank on each of them and then the final popularity is the difference between the two scores. There are some problems with separating the positive and negative edges like this. Imagine the network has a sizable number of trolls, users who purposely post annoying or abusive content and are accordingly disliked by most well intentioned users. Trolls may decide to constantly give negative votes to some well-intentioned users who may otherwise post well-received content. Trolls tend to have many negative links, and therefore are ranked highly in the negative graph, which means their negative votes would weigh heavily. This means that this simple algorithm is not good at distinguishing trolls from their victims. Ideally, earning the ire of trolls would not weigh against your popularity so these two types of edges should be considered in tandem.
The research team of Wu, Aggarwal, and Sun constructed what they call the Troll Trust model to improve upon this this algorithm for signed networks. The end result in to compute a probability that an arbitrary user might consider a specific user a to be a troll. Similar to the Page Rank algorithm, it relies on the structure of the graph to iteratively update approximations to these probabilities. It also has the desirable property that it always converges to a fixed point. As many social media websites are struggling with issues of hate speech, tools like the Troll Trust model could be used to identify users to consider banning or restricting.
Article: http://charuaggarwal.net/trolls.pdf