Computation of ring statistics for network models of solids

In random-network models of amorphous solids, ring statistics provide a measure of medium-range order. However, many criteria used so far to determine the set of rings to count have serious drawbacks. Here, a ``shortest-path'' (SP) criterion is shown to give ring statistics that agree well with intuition, and to avoid problems inherent in other criteria. The SP criterion arises naturally in a hierarchy of criteria for ``irreducible'' rings. It falls exactly midway between the least restrictive and most restrictive criteria in the hierarchy, suggesting that it may give the optimal balance between the two extremes. Since SP rings are simple to characterize and enumerate, SP ring statistics appear to be the most promising means for characterizing network topology.