  The analysis of networks characterized by links with heterogeneous intensity
or weight suffers from two long-standing problems of arbitrariness. On one
hand, the definitions of topological properties introduced for binary graphs
can be generalized in non-unique ways to weighted networks. On the other hand,
even when a definition is given, there is no natural choice of the (optimal)
scale of link intensities (e.g. the money unit in economic networks). Here we
show that these two seemingly independent problems can be regarded as
intimately related, and propose a common solution to both. Using a formalism
that we recently proposed in order to map a weighted network to an ensemble of
binary graphs, we introduce an information-theoretic approach leading to the
least biased generalization of binary properties to weighted networks, and at
the same time fixing the optimal scale of link intensities. We illustrate our
method on various social and economic networks.
