Abstract: The dissertation proposes a quaternion hyper－graph model based on complex network theory, defines a series of basic measurements on networks, investigates the degree distributions of vertices and the excess degree distribution, and constructs a new random quaternion hyper－graph model. It also explores the determinant condition of the existence of a giant component in quaternion hyper－graph. The research can be applied to analyzing the structure and topologies of the large－scale hyper－complex network in social networks.

Key words: quaternion hyper－graph, distribution of degrees, projection graphs