in the mathematical discipline of graph theory, the line graph of an undirected graph "g" is another graph "l"("g") that represents the adjacencies between edges of "g". the name line graph comes from a paper by although both and used the construction before this. other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the ϑ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph.