Finding the shortest path for a Hypergraph

A hypergraph is given by [Formula: see text], where [Formula: see text] is a set of vertices and [Formula: see text] is a set of nonempty subsets of [Formula: see text], the member of [Formula: see text] is named hyperedge. So, a hypergraph is a nature generalization of a graph. A hypergraph has a complex structure, thus some researchers try to transform a hypergraph to a graph. In this paper, we define two graphs, Clique graph and Persian graph. These relations are one to one. We can find the shortest path between two vertices in a hypergraph [Formula: see text], by using the Dijkstra algorithm in graph theory on the graphs corresponding to [Formula: see text].