First, both get_verts.py and get_edges.py import get_auth.py where you'll need to put in your twitter developer credentials. If you don't know what this means, check out this walkthrough.
# returns twitter api
# (this codeblock is in both get_auth.py files)
def getAPI():
api = twitter.Api(consumer_key="",
consumer_secret="",
access_token_key="",
access_token_secret="")
api.sleep_on_rate_limit = True
return api
Run get_verts.py on a set of twitter names to search for these names and output a list of verified twitter ids and attributes in a .csv output file. Any .csv input file with whatever you want to search for per user as the first column will work. Extra columns will be preserved in the output file. Then, to find the all edges between vertices in this set run get_edges.py on the vertex file, which outputs an edgelist file.
python get_verts.py names_to_search.csv verts_fname.csv
python get_edges.py verts_fname.csv edges_fname.csv
The twitter-graph.ipynb ipython-notebook shows a few examples of how you can programmatically generate some cool graphs and do analysis with the igraph package.