Ring statistics

The analysis of the topology of network-type structure models (liquid, crystalline or amorphous systems) is often based on the part of the structural information which can be represented in the graph theory using nodes for the atoms and links for the bonds. The absence or the existence of a link between two nodes is determined by the analysis of the total and partial radial distribution functions of the system.
In such a network a series of nodes and links connected sequentially without overlap is called a path. Following this definition a ring is therefore simply a closed path. If we study thoroughly a specific node of this network we see that this node can be involved in numerous rings. Each of these rings is characterized by its size and can be classified based upon the relations between the nodes and the links which constitute it.