The Persistent Homology Algorithm For Computing The Saddle Point In Social Networks

Social networks is a important tool for describing structures. Analysing the struc-ture of networks and understanding the properties of networks have great significance in a variety of fields. In this paper, we attempt to use the saddle points to analyse the structure of networks, dividing the networks by using the saddle points and their at-traction basin. By constructing the potential function, we generalized the definition of saddle points from the continuous potential energy field to discrete networks. Then, constructing the filtration in the networks and using the persistent homology to study the topological structure of the social networks. Finally, by computing the changes in Betti numbers we got the saddle points and show how to divide the social networks.