Two years ago I have pointed out the importance of ω-operad of coendomorphism to describe the weak ω category of the weak ω categories, up to a "contractibility hypothesis". In fact this technology of ω-operads of coendomorphism can be adapted for many higher structures, without any hypotheses : For instance we are going to describe the ω-graph of the ω-graphs, the reflexive ω-graphs of the reflexive ω-graphs, the ω-magma of the ω-magmas, and the reflexive ω-magma of the reflexive ω-magmas, all that by using the same technology, where ω-operads of coendomorphism play a central role.