A hypergraph is linear if any two edges have at most one common vertex. Two edges are r-intersecting if they share at least r common vertices. A k-uniform hypergraph is hypegraph with each edge of size k. Note that simple graphs are linear 2-uniform hypergraphs (a simple graph is loopless and contains no multiple edges). The intersection graph of a graph is usually called as Line graph. The characterization of Line graphs was solved by Van Rooij and Wilf and by Beineke.