Finding the shortest path for a Hypergraph

A hypergraph is given by H = (V, E), where V is a set of vertices and E is a set of nonempty subsets of V, the member of E 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 H, by using the Dijkstra algorithm in graph theory on the graphs corresponding to H.