Q:

Using Boost Graph Library (BGL) to identify connected components

I am trying to use the Boost Ggraph Library. On each iteration of my program, I have a set of points, e.g. {1,2,3,4,5,6,7,8,9,10} on iteration one and {1,2,3,...,1000} on iteration two, ...
For each point I know which other points it is connected to, e.g. at iteration one every point is connected as below:
c(1)={3,5,7,8}   
c(2)={}   
c(3)={1,4,10}   
c(4)={3}    
c(5)={1,9}   
c(6)={}    
c(7)={1,8}    
c(8)={1,7}    
c(9)={5}    
c(10)={3}    

Each point has a property, e.g. p(1)=10, p(2)=100, p(3)=20, ...
How can I create an undirected graph in Boost and iterate over the connected component(s)?

A:

You will need to include the following headers:
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/connected_components.hpp>

Then you need to declare a type for your graph. The following is suitable for the requirements you gave, however you might want to consult this page to learn more about other choices for template parameters:
typedef
  boost::adjacency_list<
    boost::vecS            // edge list
  , boost::vecS            // vertex list
  , boost::undirectedS     // directedness
  , float                  // property associated with vertices
  >
Graph;

You may create a graph with a given number of points, and you may later add more points:
Graph c (10);              // create a graph with 10 points
boost::add_vertex (c);     // add a vertex to the graph

To add edges use (note that vertices are enumerated starting from 0):
boost::add_edge (0, 1, c); // add an edge between vertices 0 and 1 in the graph

Finally, with the following piece of code you may compute connected components in your graph:
std::vector<int> component (boost::num_vertices (c));
size_t num_components = boost::connected_components (c, &component[0]);

The value returned from the function is the number of found components. Each item in component vector will be set to the component id of the corresponding vertex. This means that you can iterate over it and e.g. print the vertices that belong to a particular component:
std::cout << "Vertices in the first component:" << std::endl;
for (size_t i = 0; i < boost::num_vertices (c); ++i)
  if (component[i] == 0)
    std::cout << i << " ";

