  In this paper, we describe {\sc quantitative graph theory} and argue it is a
new graph-theoretical branch in network science, however, with significant
different features compared to classical graph theory. The main goal of
quantitative graph theory is the structural quantification of information
contained in complex networks by employing a {\it measurement approach} based
on numerical invariants and comparisons. Furthermore, the methods as well as
the networks do not need to be deterministic but can be statistic. As such this
complements the field of classical graph theory, which is descriptive and
deterministic in nature. We provide examples of how quantitative graph theory
can be used for novel applications in the context of the overarching concept
network science.
