Let G be a graph of order n satisfying that there exists lambda epsilon Z(+) for which every graph of order n and size t is contained in exactly. distinct subgraphs of the complete graph K-n isomorphic to G. Then G is called t-edge-balanced and. the index of G. In this article new examples of 2-edge-balanced graphs are constructed from bipartite graphs and some further methods are introduced to obtain more from old. (C) 2015 Wiley Periodicals Inc.