For a given graph G = (V,E) and a positive integer k, the super line graph of index k of G is the graph Sk(G) which has for vertices all the k-subsets of E(G), and two vertices S and T are adjacent whenever there exist s \varepsilon S and t \varepsilon T such that s and t share a common vertex. In the super line multigraph Lk(G) we have an adjacency for each such occurrence.

We give a formula to find the adjacency matrix of L_k(G). If G is a regular graph, we calculate all the eigenvalues of L_k(G) and their multiplicities. From those results we give an upper bound on the number of isolated vertices.