Connected Components BOOST c++

Question

If I have a graph with 1 node and no edges. the the number of connected components = 1,right?

If I have a graph with 2 node and no edges. the the number of connected components = 2,right?

If I have a graph with 2 node and 1 edges. the the number of connected components = 1,right?

I have this peice of code :

typedef adjacency_list <vecS, vecS, undirectedS> Graph;
    typedef graph_traits < Graph >::edge_descriptor Edge;

   /* typedef graph_traits<Graph>::vertex_descriptor Vertex;
    typedef property_map<Graph, vertex_index_t>::type IndexMap;

    typedef std::pair<int,int> E;
    typedef graph_traits<Graph>::vertex_iterator vertex_iter;
    typedef graph_traits<Graph>::out_edge_iterator edge_iter;
    typedef property_map<Graph, vertex_index_t>::type VertexIndexMap;
    typedef property_map<Graph, edge_weight_t>::type EdgeWeightMap;*/


  int main(int,char*[])
  {

   int num_nodes,num_edges;
   cin >> num_nodes >> num_edges;

   Graph g(num_nodes);

    for(int i = 0;i < num_edges; i++) // i/p edges into graph g
    {

        int e1,e2;
        cin >> e1 >> e2;

        Edge e;
        bool success;


        tie(e,success) = add_edge(e1, e2, g);
    }

    vector <int> components(num_nodes);
    int num = connected_components(g, &components[0]);




        cout<<"moooooo"<<num<<endl;

for these inputs :

1 0

and

2 0

and

2 1

I get respectively

1

and

2

and

2

why? shoudn't it be 1 now? Have I misunderstood connected components?

My program gives num=2 for all inputs,my inputs are the following:

4 3
1 2
2 3
3 4

4 4
1 2
2 3
3 4
4 1

5 5
1 2
2 3
3 4
4 1
3 5

6 6
1 2
2 3
3 4
4 1
3 5
5 6

8 9
1 2
2 3
3 4
4 1
3 5
5 6
6 7
7 8
8 5

8 10
1 2
2 3
3 4
4 1
3 5
5 6
6 7
7 8
8 5
4 6

what shpudl I do?

Answer 1

A connected component is a subgraph of a graph or the graph itself where we can reach all the nodes from every other node. The minimum number of connected component is =0,whereas the maximum is the number of nodes of the graph.

The problem here was that I used node starting from 1.... and boost considers nodes from 0,hence I always got 1 connected component more than normal.

The trick :: is to use vertice_num_ -1 instead of the vertice number itself.