Relaxing the strong triadic closure problem for edge strength inference

Florian Adriaens*, Tijl De Bie, Aristides Gionis, Jefrey Lijffijt, Antonis Matakos, Polina Rozenshtein

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
52 Downloads (Pure)


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 to obtain. 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). They exploited this property to formulate the inference of the strength of social ties as a NP-hard maximization problem, and proposed two approximation algorithms. We refine and improve this line of work, by developing a sequence of linear relaxations of the problem, which 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 one to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. Moreover, these relaxations allow us to easily change the objective function to more sensible alternatives, instead of simply maximizing the number of strong edges. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, while at the same time questioning the validity of leveraging the STC property for edge strength inference in practice.

Original languageEnglish
Pages (from-to)611-651
Number of pages41
JournalData Mining and Knowledge Discovery
Issue number3
Publication statusPublished - May 2020
MoE publication typeA1 Journal article-refereed


  • Convex relaxations
  • Half-integrality
  • Linear programming
  • Strength of social ties
  • Strong triadic closure

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