  Granovetter's weak ties theory is a very important sociological theory
according to which a correlation between edge weight and the network's topology
should exist. More specifically, the neighbourhood overlap of two nodes
connected by an edge should be positively correlated with edge weight (tie
strength). However, some real social networks exhibit a negative correlation -
the most prominent example is the scientific collaboration network, for which
overlap decreases with edge weight. It has been demonstrated that the
aforementioned inconsistency with Granovetter's theory can be alleviated in the
scientific collaboration network through the use of asymmetric measures. In
this paper, we explain that while asymmetric measures are often necessary to
describe complex networks and to confirm Granovetter's theory, their
interpretation is not simple, and there are pitfalls that one must be wary of.
The definitions of asymmetric weights and overlaps introduce structural
correlations that must be filtered out. We show that correlation profiles can
be used to overcome this problem. Using this technique, not only do we confirm
Granovetter's theory in various real and artificial social networks, but we
also show that Granovetter-like weight-topology correlations are present in
other complex networks (e.g. metabolic and neural networks). Our results
suggest that Granovetter's theory is a sociological manifestation of more
general principles governing various types of complex networks.
