BFS (THE RIGHT ONE)

    public static <T> List<Vertex<T>> breadthFirstSearch(Vertex<T> start,
            Graph<T> graph) {

        if (start == null || graph == null) {
            String msg = "The start Vertex or the graph cannot equal null.";
            throw new IllegalArgumentException(msg);
        }

        if (graph.getAdjacencyList().get(start) == null) {
            String msg = "The start vertex must exist in the graph";
            throw new IllegalArgumentException(msg);
        }

        List<Vertex<T>> order = new java.util.ArrayList<Vertex<T>>();
        Set<Vertex<T>> visited = new java.util.HashSet<Vertex<T>>();
        Queue<Vertex<T>> level = new LinkedList<Vertex<T>>();

        order.add(start);
        visited.add(start);
        level.add(start);

        while (!level.isEmpty()) {
            Vertex<T> v = level.remove();

            for (VertexDistancePair<T> pair : graph.getAdjacencyList().get(v)) {
                Vertex<T> current = pair.getVertex();
                if (!visited.contains(current)) {
                    visited.add(current);
                    order.add(current);
                    level.add(current);
                }
            }
            //level = nextLevel;
        }
        return order;
    }