  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.
