  Networks are important representations in computer science to communicate
structural aspects of a given system of interacting components. The evolution
of a network has several topological properties that can provide us information
on the network itself. In this paper, we present a methodology to compare the
the topological characteristics of the evolution of a network, encoded into a
(persistence) diagram that tracks the lifetimes of those features. This will
enable us to classify the evolution of networks based on the distance between
the diagrams that represent such network evolution. In that, we also consider
complex vectors that bring a complementary perspective to the distance-based
classification that is closer to the computational methods, aims to enhance the
computational efficiency of those comparisons, and that is by itself a source
of open research questions.
