  The new concept of multilevel network is introduced in order to embody some
topological properties of complex systems with structures in the mesoscale
which are not completely captured by the classical models. This new model,
which generalizes the hyper-network and hyper-structure models, fits perfectly
with several real-life complex systems, including social and public
transportation networks. We present an analysis of the structural properties of
the multilevel network, including the clustering and the metric structures.
Some analytical relationships amongst the efficiency and clustering coefficient
of this new model and the corresponding parameters of the underlying network
are obtained. Finally some random models for multilevel networks are given to
illustrate how different multilevel structures can produce similar underlying
networks and therefore that the mesoscale structure should be taken into
account in many applications.
