Case for trust is similar to the transitivity of trust. We note though that the stronger the relations between 1 and 2, and 2 and 3, the more likely it is that 1 and 3 are positively linked. If 1&2, or 2&3 are weak ties and as a result do not spend any time together, then there is no pressure on 1&3 to be friends.

The case for distrust emphasizes the lack of homophily causes a tension to distrust. If 2&3 are very close friends, but 1&2 hate each other, there is pressure on 1&3 to distrust each other through influence of 2 on 3. However, if the distrust between 1&2 or the relationship between 2&3 are not strong, there is less of a likelihood, that these relationships will have an effect on the relationship between 1&3.

We formalize our theory and the notion of convergence using the Metric Multidimensional Scaling problem. Our novel method has sound social and psychological basis, and captures the classical balance theory as a special case. We show that given a network, we can solve the edge sign prediction problem, i.e. finding if two people trust each other or have distrust, using a stress majorization (SM) algorithm. Using the datasets studied in past work, we show that our methods match and significantly outperform state of the art in trust prediction.

Software is available at