Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems

In a first part we present the state of the art of the ring statistics when used to study the structural properties of solids. The different possibilities used to classify rings when analysing a material using the graph theory framework are presented. Afterwards a new and original method is proposed to analyse the connectivity of a topological network using ring statistics. This method allows to obtain the connectivity profile of the network and then to study and compare with efficiency the connectivity of different networks using ring statistics. Then a detailed analysis of SiO2 and GeS2 amorphous samples obtained using molecular dynamics is proposed to illustrate the main features of our method. A FORTRAN 90 code mainly devoted to the ring statistics analysis of materials with an implementation of the present method is also presented.