In recent years, in different fields, it has become possibile to observe large collections of networks
referring to the same phenomenon, e.g. sets of collaboration networks, each describing different
scientific field; sets of ego networks, where egos belong to the same category; sets of governance
networks; sets of brain networks. Given such sets of networks, it could be of interest the comparison of
net- works among each other. At the same time it could be relevant the detection of a small number of
representative networks that can serve as a condensed view of the entire collection of networks. In this
paper we focus on this latter aim which amounts, in a statistical perspective, in finding what would be
called prototypical networks able to typify the network structures starting from the observed ones. To
this aim, we adopt the approach proposed in Ragozini et. al, (2016) in the framework the analysis of N
statistical statistical units, described by p variables, synthesized by a set m prototypes. The procedure we
propose goes through 3 steps: i) describe a network through a mixture of features referring to local,
global, and intermediate-scale (meso-scale) network structure ii) find in the space of descriptors a set of
prototypes by applying the procedure proposed in Ragozini et. al, (2016); iii) find in the original space of
the networks, on the base of results of the previous steps, the prototypical networks and profile them.
This procedure allows us to typify the most characteristic network structures in the observed set of
networks, and to have prototypical networks that are characterized by clear and interpretable profiles in
terms of their most relevant features and their specificity in contrast to the others. We demonstrate via a
simulation study how the proposed procedure is able to discriminate and describe different types of
networks derived from several generative models.
