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Social networks often provide only a binary perspective on social ties: twoindividuals are either connected or not. While sometimes external informationcan be used to infer the strength of social ties, access to such informationmay be restricted or impractical. Sintos and Tsaparas (KDD 2014) firstsuggested to infer the strength of social ties from the topology of the networkalone, by leveraging the Strong Triadic Closure (STC) property. The STCproperty states that if person A has strong social ties with persons B and C, Band C must be connected to each other as well (whether with a weak or strongtie). Sintos and Tsaparas exploited this to formulate the inference of thestrength of social ties as NP-hard optimization problem, and proposed twoapproximation algorithms. We refine and improve upon this landmark paper, bydeveloping a sequence of linear relaxations of this problem that can be solvedexactly in polynomial time. Usefully, these relaxations infer more fine-grainedlevels of tie strength (beyond strong and weak), which also allows to avoidmaking arbitrary strong/weak strength assignments when the network topologyprovides inconclusive evidence. One of the relaxations simultaneously infersthe presence of a limited number of STC violations. An extensive theoreticalanalysis leads to two efficient algorithmic approaches. Finally, ourexperimental results elucidate the strengths of the proposed approach, andsheds new light on the validity of the STC property in practice.

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