From acquaintance to best friend forever: robust and fine-grained inference of social tie strengths.

Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer the emph{strength} of social ties, access to such information may be restricted or impractical. and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the emph{Strong Triadic Closure (STC)} property. %---postulated to hold in social networks~cite{sim:08}. The STC property states that if person $A$ has strong social ties with persons $B$ and $C$, $B$ and $C$ must be connected to each other as well (whether with a weak or strong tie). Sintos and Tsaparas exploited this to formulate the inference of the strength of social ties as NP-hard optimization problem, and proposed two approximation algorithms. We refine and improve upon this landmark paper, by developing a sequence of linear relaxations of this problem that can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. One of the relaxations simultaneously infers the presence of a limited number of STC violations. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, and sheds new light on the validity of the STC property in practice.