Bonding patterns in tridehydrobenzenes are studied by electronic structure calculations. In all three isomers, the unpaired electrons form partial bonds between the radical centers. The strength of these bonds varies from a rather weak (but stabilizing) interaction of about 0.5 kcal/mol up to 32 kcal/mol, which is one-third of a typical chemical bond energy. The structural signature of these bonds is shorter distances between the radical centers relative to the closed-shell precursor. A doublet ground state is another manifestation of stabilizing interactions of unpaired electrons.