Dense ‘‘diamondlike’’ hydrocarbon films (a-C:H) are a class of amorphous solids which can be condensed as thin films from nonequilibrium environments by several plasma deposition techniques. Films with hydrogen atom fractions from 0.5 to 0.6 select a structure with an average coordination number close to the theoretical value at which stabilization by bonding and destabilization by strain energy are balanced. This coordination number is achieved by the incorporation of the hydrogen and by the presence of trigonally (sp2) bonded carbon in the carbon skeletal network. Theory predicts a range of hydrogen atom fraction, outside of which fully constrained, random hydrocarbon networks cannot exist. The dense hydrocarbon films show extreme values of physical properties, including hardness and argon diffusivity, which can be related to their unusual structure.