A vast array of experimental data on water provides a global view of the liquid that implicates its tetrahedral hydrogen-bonding network as the unifying molecular connection to its observed structural, thermodynamic, and dielectric property trends with temperature. Recently the classification of water as a tetrahedral liquid has been challenged based on X-ray absorption (XAS) experiments on liquid water (Ph. Wernet et al., Science, 2004, 304, 995), which have been interpreted to show a hydrogen-bonding network that replaces tetrahedral structure with chains or large rings of water molecules. We examine the consequences of tetrahedral vs. chain networks using three different modified water models that exhibit a local hydrogen bonding environment of two hydrogen bonds (2HB) and therefore networks of chains. Using these very differently parameterized models we evaluate their bulk densities, enthalpies of vaporization, heat capacities, isothermal compressibilities, thermal expansion coefficients, and dielectric constants, over the temperature range of 235–323 K. We also evaluate the entropy of the 2HB models at room temperature and whether such models support an ice I_h structure. All show poor agreement with experimentally measured thermodynamic and dielectric properties over the same temperature range, and behave similarly in most respects to normal liquids.