The time complexity of implementation of BFS and connected-graph-boolean

I would like to verify whether this implementation of BFS and a method, which returns a boolean whether a graph is connected runs in O(n^2) or some better time:

 public static Map<Vertex, Boolean> bfs(Vertex start) {           Map<Vertex, Boolean> visited = g.createVertexMap(false);           Queue<Vertex> q = new LinkedList<Vertex>();           visited.put(start, true);           q.offer(start);           while (!q.isEmpty()) {                   Vertex v = q.poll();                   for (Vertex neighbour : v.getOutNeighbours()) {                       counter++;                           if (!visited.get(neighbour)) {                                   visited.put(neighbour, true);                                   q.offer(neighbour);                           }                   }           }           return navstiveny;   }      public static boolean isConnected() {         Vertex someVertex = g.getVertices().iterator().next();         Map<Vertex, Boolean> availability = bfs(someVertex);         return !availability.values().contains(false);     }