Confronto tra omologia persistente e statistica-simpliciale di sistemi complessi

Many real systems have been studied in the last decades in the form of complex networks. There are many properties that can be analyzed in order to understand the structure of these system: graph theory and statistical mechanics give many ways and models to try to study them. Another efficient tool to analyze complex networks is given by a very the- oretical mathematical sector: topology. This field of math studies qualitative properties of space such as continuity and connectivity. Topology can be applied to complex networks, and in this work we focus on two main tools of this branch: the simplicial and the persistent homology. Simplicial homology provides information on connectivity of spaces made of simplicial complexes, while persistent homology computes long lived topo- logical features. In this work we compare these methods applied to a set of real networks.