In some graphs, edges are directed. In other graphs, edges are undirected. Whether edges are directed all depend on how a graph is used, and what it represents.
It is possible, however, to represent all graphs using directed edges. If a graph does not require directed edges, then we can used edge pairs. In other words, if vertex v and w are connected, and there is no need to indicate direction, then we can use (v,w) and (w,v) to represent the connection.