In this paper,DFT method was used to study the relative stability of hydrogen bonding networks of numerous 512,51262 and 435663 water cluster isomers.Herein we introduced an optimized six-digit definition to characterize diverse sub-grouped hydrogen bonds to consider the cooperative effect of the nearest and next-nearest neighbor water molecules.There are totally 74 kinds of sub-grouped hydrogen bonds in cage hydrate clusters,and these energies can be obtained by iterative calculations.This improvement effectively explains some regularity contained in hydrogen bonding cooperative effect.In general,donor or acceptor fragment sharing identical value of three independent digits usually performs poor cooperative effect,indicating that the existence of those same-digital-array fragments is the necessary condition to judge poor cooperative effect.Vice versa,the existence of different-digital-array is also the necessary condition to judge strong cooperative effect.