In this paper we unify the developments of Batanin , Batanin-Weber  and Cheng  into a single framework in which the interplay between multitensors on a category $V$, and monads on the category $\cal G V$ of graphs enriched in $V$, is taken as fundamental. The material presented here is the conceptual background for subsequent work: in Batanin-Cisinski-Weber  the Gray tensor product of 2-categories and the Crans  tensor product of Gray categories are exhibited as existing within our framework, and in Weber  the explicit construction of the funny tensor product of categories is generalised to a large class of Batanin operads.
Keywords: multitensors, enriched graphs, higher categories, higher operads
2010 MSC: 18A05; 18D20; 18D50; 55P48
Theory and Applications of Categories, Vol. 28, 2013, No. 26, pp 857-932.