  Completely positive graphs have been employed to associate with completely
positive matrices for characterizing the intrinsic zero patterns. As tensors
have been widely recognized as a higher-order extension of matrices, the
multi-hypergraph, regarded as a generalization of graphs, is then introduced to
associate with tensors for the study of complete positivity. To describe the
dependence of the corresponding zero pattern for a special type of completely
positive tensors--the $\{0,1\}$ completely positive tensors, the completely
positive multi-hypergraph is defined. By characterizing properties of the
associated multi-hypergraph, we provide necessary and sufficient conditions for
any $(0,1)$ associated tensor to be $\{0,1\}$ completely positive. Furthermore,
a necessary and sufficient condition for a uniform multi-hypergraph to be
completely positive multi-hypergraph is proposed as well.
