Ink composition containing a particular type of dye, and corresponding ink jet printing process

An ink composition is disclosed which contains a novel type of dye (DYE)n(SAU)m that is capable of self-assembling under appropriate conditions, or is capable of assembling with another analogous dye (DYE')n'(SAU')m', or is capable of assembling with a compound (SAU'')p(X)q, thus forming supramolecular structures. Also disclosed is an ink jet printing process using these novel dyes, and an ink jet printing apparatus provided with an ink cartridge containing such a dye.