The properties of hydrogen bond networks in ambient, supercritical, and stretched model water at temperatures between 573 K and 873 K and densities between 0.1 g/cm(3) and 1 g/cm(3) have been investigated by molecular dynamics simulation. A flexible simple point charged pair potential model has been used and, after comparing two hydrogen bond definitions, a pure geometrical criterion has been employed. The structure found agrees well with recent experimental data. The presence of hydrogen bonds has been detected at every supercritical state, although the tetrahedral structure typical of liquid water at room temperature is substituted in supercritical model water by chains of hydrogen-bonded molecules allowing cavities. The calculated OH stretching peak shifts toward higher values when changing from ambient to supercritical conditions. Nevertheless, under such changes bending and libration bands are displaced to lower frequencies. The cage effect typical of liquid water at ambient conditions does not appear in the supercritical states.