  Granovetter's weak tie theory of social networks is built around two central
hypotheses. The first states that strong social ties carry the large majority
of interaction events; the second maintains that weak social ties, although
less active, are often relevant for the exchange of especially important
information (e.g., about potential new jobs in Granovetter's work). While
several empirical studies have provided support for the first hypothesis, the
second has been the object of far less scrutiny. A possible reason is that it
involves notions relative to the nature and importance of the information that
are hard to quantify and measure, especially in large scale studies. Here, we
search for empirical validation of both Granovetter's hypotheses. We find clear
empirical support for the first. We also provide empirical evidence and a
quantitative interpretation for the second. We show that attention, measured as
the fraction of interactions devoted to a particular social connection, is high
on weak ties --- possibly reflecting the postulated informational purposes of
such ties --- but also on very strong ties. Data from online social media and
mobile communication reveal network-dependent mixtures of these two effects on
the basis of a platform's typical usage. Our results establish a clear
relationships between attention, importance, and strength of social links, and
could lead to improved algorithms to prioritize social media content.
