  Though commonly found in the real world, directed networks have received
relatively less attention from the literature in which concerns their
topological and dynamical characteristics. In this work, we develop a magnetic
Laplacian-based framework that can be used for studying directed complex
networks. More specifically, we introduce a specific heat measurement that can
help to characterize the network topology. It is shown that, by using this
approach, it is possible to identify the types of several networks, as well as
to infer parameters underlying specific network configurations. Then, we
consider the dynamics associated with the magnetic Laplacian as a means of
embedding networks into a metric space, allowing the identification of
mesoscopic structures in artificial networks or unravel the polarization on
political blogosphere. By defining a coarse-graining procedure in this metric
space, we show how to connect the specific heat measurement and the positions
of nodes in this space.
