An undirected graph has edges that are unordered pairs of vertices. In a simple undirected graph there are no loops or multiple edges. The skeleton of a directed graph forgets the directions of its edges and is an undirected graph.
Multiple edges are distinct edges with the same pair of endpoint vertices in an undirected graph. A multigraph permits them; a simple graph does not. In an orientation of a graph of a multigraph, each such edge receives its own direction, so two of them can supply opposite directed edges between the same vertices.
