Generate Geometric Random Graphs and check the connectivity

I want to re-generate the graph below which consists of several nodes (say 1000) that's connected the program will do the random graph then check if its connected or not then I want to generate a connectivity graph for all the graphs done before and were connected with respect to the value r
like in the picture below

I would like to use java programming language or python whatever easies, but I dont know how to start and what to do