A fractal hypernetwork model with good controllability

Fractal is a common feature of many deterministic complex networks. The complex networks with fractal features have interesting structure and good performance. The network based on hypergraph is named hypernetwork. In this paper, we construct a hypernetwork model with fractal properties, and obtain its topological properties. Moreover, according to the exact controllability theory, we obtain the node controllability and the hyperedge controllability of the fractal hypernetwork. The simulation results show that the measure of hyperedge controllability is smaller than that of node in the fractal hypernetwork. In addition, We compare the controllability of three types of hypernetwork, which are easier to control by their hyperedges. It is shown the fractal hypernetwork constructed in this paper has the best controllability. Because of the good controllability of our fractal hypernetwork model, it is suitable for the topology structure of many real systems.