A methodology to evaluate the evolution of networks using topological\n data analysis

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