### The R.I.N.G.S. code is the ideal tool to study and to analyze the connectivity of a material using the graph theory framework.

When studying amorphous systems ring statistics are mainly used to obtain informations inaccessible using standard tools such as the radial distribution functions or the neutron structure factors.

In particular it allows to scan the network at a farther scale than the first or the second coordination shell. Thus it is possible to obtain informations on the intermediate Range Order 'IRO' of the material.

For instance it is well known that in glass science finding the origin of the disorder and understanding the origin of the IRO is a key for the interpretation of the optical and conduction phenomena.

In this context using the ring statistics techniques appears to be fully justified.

In this context we have developed the R.I.N.G.S. code to implement and compare the different possibility to classify rings existing in the literature [a, b, c, d, e, f].

Nevertheless precise informations can not be obtained without using an accurate method.

In the R.I.N.G.S. code we have implemented an original method to analyze the connectivity of a topological network using ring statistics [h].

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.

The part of the R.I.N.G.S. code dedicated to the ring statistics is presented in figure [Fig. 1]

The analysis regarding the different types of rings (King, shortest paths, primitive and strong rings).

Furthermore figure [Fig. 1] illustrates that the R.I.N.G.S. code does not focus only on the connectivity, i.e. finding the rings, but also on the physical properties which can be deduced from the analysis.

**Figure 1: ** Rings statistics in the RINGS code - simplified structure

- a
- S. V. King.
*Nature*,**213**:1112 (1967). - b
- D. S. Franzblau.
*Phys. Rev. B*,**44**(10):4925-4930 (1991). - c
- L. Guttman.
*J. Non-Cryst. Solids.*,**116**:145-147 (1990). -
- d
- K. Goetzke and H. J. Klein.
*J. Non-Cryst. Solids.*,**127**:215-220 (1991). - e
- X. Yuan and A. N. Cormack.
*Comp. Mat. Sci.*,**24**:343-360 (2002). - f
- F. Wooten.
*Acta Cryst. A*,**58**(4):346-351 (2002). - g
- S. Le Roux and P. Jund.
*?????????????***??**(?):????-???? (2009).

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