Using strong triadic closure to characterize ties in social networks

In the past few years there has been an explosion of social networks in the online world. Users flock these networks, creating profiles and linking themselves to other individuals. Connecting online has a small cost compared to the physical world, leading to a proliferation of connections, many of which carry little value or importance. Understanding the strength and nature of these relationships is paramount to anyone interesting in making use of the online social network data. In this paper, we use the principle of Strong Triadic Closure to characterize the strength of relationships in social networks. The Strong Triadic Closure principle stipulates that it is not possible for two individuals to have a strong relationship with a common friend and not know each other. We consider the problem of labeling the ties of a social network as strong or weak so as to enforce the Strong Triadic Closure property. We formulate the problem as a novel combinatorial optimization problem, and we study it theoretically. Although the problem is NP-hard, we are able to identify cases where there exist efficient algorithms with provable approximation guarantees. We perform experiments on real data, and we show that there is a correlation between the labeling we obtain and empirical metrics of tie strength, and that weak edges act as bridges between different communities in the network. Finally, we study extensions and variations of our problem both theoretically and experimentally.