  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 strength of social ties, access to such information
may be restricted or impractical. Sintos and Tsaparas (KDD 2014) first
suggested to infer the strength of social ties from the topology of the network
alone, by leveraging the Strong Triadic Closure (STC) property. 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.
