Inferring Tie Strength in Temporal Networks

TL;DR

The paper tackles inferring tie strength in temporal networks by generalizing the strong triadic closure (STC) to weighted settings and extending STC+ with edge additions. It introduces a sliding-window streaming framework that maintains a 2-approximation for WeightedMinSTC and a 3-approximation for WeightedMinSTC+ by reducing the problem to minimum weight vertex covers on wedge graphs and, for STC+, wedge hypergraphs; a fully dynamic $k$-approximation for MWVC in $k$-uniform hypergraphs is developed as a key component. The authors provide ILP formulations for exact solutions, design weighting functions that reflect empirical tie strength, and demonstrate that the weighted STC/ STC+ better align with edge weights while enabling scalable processing on real-world data. Empirical results on diverse temporal networks show improved alignment with a priori information and significant speedups of the streaming approach over recomputation, highlighting practical applicability for large-scale, dynamic social data.

Abstract

Inferring tie strengths in social networks is an essential task in social network analysis. Common approaches classify the ties as wea} and strong ties based on the strong triadic closure (STC). The STC states that if for three nodes, $A$, $B$, and $C$, there are strong ties between $A$ and $B$, as well as $A$ and $C$, there has to be a (weak or strong) tie between $B$ and $C$. A variant of the STC called STC+ allows adding a few new weak edges to obtain improved solutions. So far, most works discuss the STC or STC+ in static networks. However, modern large-scale social networks are usually highly dynamic, providing user contacts and communications as streams of edge updates. Temporal networks capture these dynamics. To apply the STC to temporal networks, we first generalize the STC and introduce a weighted version such that empirical a priori knowledge given in the form of edge weights is respected by the STC. Similarly, we introduce a generalized weighted version of the STC+. The weighted STC is hard to compute, and our main contribution is an efficient 2-approximation (resp. 3-approximation) streaming algorithm for the weighted STC (resp. STC+) in temporal networks. As a technical contribution, we introduce a fully dynamic $k$-approximation for the minimum weighted vertex cover problem in hypergraphs with edges of size $k$, which is a crucial component of our streaming algorithms. An empirical evaluation shows that the weighted STC leads to solutions that better capture the a priori knowledge given by the edge weights than the non-weighted STC. Moreover, we show that our streaming algorithm efficiently approximates the weighted STC in real-world large-scale social networks.

Figures (6)

• Figure 1: Example for the difference between weighted and non-weighted STC. Strong edges are highlighted in red, and weak edges are dashed.
• Figure 2: Example for temporal graph $\mathcal{G}\xspace$, the aggregated graph $A_\phi(\mathcal{G}\xspace)$, the wedge graph $W(A_\phi(\mathcal{G}\xspace))$, and minimum weight STC.
• Figure 3: Example for computing the weighted STC of a sliding time window.
• Figure 4: Precision and recall for classifying the top-$100$ highest weighted edges in the aggregated graph as strong edges using the algorithms for the STC. The $y$-axis of precision is logarithmic.
• Figure 5: Effect of $\alpha$ on the ratio of strong edges and the normalizes sum of the weight of strong edges.

Theorems & Definitions (15)

• Definition 1
• Lemma 1
• proof
• Lemma 2
• proof
• Definition 2
• Lemma 3
• Lemma 4
• proof
• proof : Proof of \ref{['lemma:dynamic']}