Relaxing the strong triadic closure problem for edge strength inference

Abstract

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

Strengthening ties towards a highly-connected world

“…Subsequently, Rozenshtein et al (2017) consider the problem of the inference of social tie strength, while also taking community structure into account. A recent work by Adriaens et al (2020) builds directly on the stc-inference problem posed by Sintos and Tsaparas by extending and relaxing their formulation via introducing new constraints and integer labels. While these works use the stc property in order to characterize the ties currently present in the network, we view the stc property as a process that takes place in the network and leads to the creation of new edges.…”

“…In one of the first works, Sintos and Tsaparas (2014) search for an assignment of tie strengths, which maximizes the number of strong edges, while ensuring that the stc property is respected over the whole network. Subsequent works refined this methodology by studying less rigid versions of the stc property (Adriaens et al 2020), as well as considering the interplay with community structure (Rozenshtein et al 2017).…”

“…Subsequent works refined this methodology by studying less rigid versions of the property (Adriaens et al. 2020 ), as well as considering the interplay with community structure (Rozenshtein et al. 2017 ).…”

Inferring Tie Strength in Temporal Networks

“…Rozenshtein et al [41] discuss the STC with additional community connectivity constraints. Adriaens et al [1] proposed integer linear programming formulations and corresponding relaxations. Very recently, Matakos et al [31] proposed a new problem that uses the strong ties of the network to add new edges and increase its connectivity.…”

“…For the exact computation of the weighted STC, we provide an ILP formulation similar to the formulation of the unweighted version of the maximum STC problem [1]. We use binary variables x ij which encode the if edge {i, j} ∈ E is strong (x ij = 1) or weak (x ij = 0).…”