The AdjacencyGraph<TVertex, TEdge>, also known as adjacency list provides an efficient data structure to access the out edges of a vertex. This class is mutable, serializable, cloneable and can be constructed in many different ways. Internally, the data structure keeps a dictionary from TVertex to a unordered list of TEdge elements.

var graph = new AdjacencyGraph<int, Edge<int>>();
...
foreach(var vertex in graph.Vertices)
    foreach(var edge in graph.OutEdges(vertex))
        Console.WriteLine(edge);

If you need to access in-edges as well, consider using the BidirectionalGraph.