Summary: We define the new concept of the central graph of a graph \(G\) and present results about the number of edges in the central graphs of cycles and complete bigraphs and the maximum degree of a central graph. We also prove results related to the property of connectedness of a central graph. We prove a necessary condition on \(G\) to have an Eulerian central graph and the Hajos union of a graph and its central graph to be Eulerian. Harmonious colouring on the central graph of \(C_n\) and \(K_{m,n}\) is discussed and we obtain the harmonious chromatic number of the central graphs of \(C_n \) and \(K_{m,n}\) .