To evaluate the relevance of treating the hydrogen bonds in liquid water as a digital (discrete) network and applying topological analyses, a framework to optimize the fitting parameters in various hydrogen bond definitions of liquid water is proposed. Performance of the definitions is quantitatively evaluated according to the reproducibility of hydrogen bonding in the inherent structure. Parameters of five popular hydrogen bond definitions are optimized, for example. The optimal choice of parameters for the hydrogen bond definitions accentuates the binary nature of the hydrogen bonding and the intrinsic network topology of liquid water, especially at the low temperature region. The framework provides a solid basis for network analyses, which have been utilized for water, and is also useful for designing new hydrogen bond definitions.