A magic graph is a graph whose edges are labelled by  the first q positive integers, where q is the number of edges, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex; or it is a graph that has such a labelling.
A magic graph is defined as a graph where the edges are assigned unique labels from 1 to q, with q being the number of edges, and this labeling ensures that the sum of edge weights over any vertex remains consistent, regardless of which vertex is chosen; or it is characterized by such label assignment.